Equation Solver - Free Online Tool

Result

Equation

Type

Discriminant

Roots

About Equation Solver — Equation Solver Online

The Oneyfy equation solver online solves linear equations in the form ax + b = 0 and quadratic equations in the form ax² + bx + c = 0. Enter the coefficients and the solver computes the root(s) instantly — including real roots, repeated roots, and complex (imaginary) conjugate roots when the discriminant is negative. Results include the equation type, discriminant value, and the exact root values displayed in a clear results panel.

Students, teachers, engineers, and professionals use an equation solver online to verify hand-calculated algebra, check textbook answers, explore how changing coefficients affects roots, and solve equations that arise in practical contexts — physics problems, financial calculations, geometric relationships, and engineering formulas. Rather than working through the quadratic formula manually (which is error-prone with decimal coefficients), entering the values here gives an immediate, accurate result to check against or build upon.

How to Use the Equation Solver

Choose the equation type using the buttons: Linear: ax + b = 0 for first-degree equations, or Quadratic: ax² + bx + c = 0 for second-degree equations.
Enter the coefficient a in the first field. For linear equations, this is the coefficient of x; for quadratic equations, this is the coefficient of x². Note: a must not be zero for either equation type to be valid.
Enter the coefficient b — the coefficient of x (or the constant term in a linear equation).
For quadratic equations, enter the coefficient c — the constant term.
Click Solve (or press Enter in any coefficient field) — the result panel updates immediately showing the full equation, equation type, discriminant, and root(s).
Click Copy Result to copy the full result to your clipboard for pasting into notes or a document.

Understanding the Results

The results panel provides four pieces of information that fully characterise the equation's solution.

Equation: The equation as entered, displayed in standard form (e.g. 2x^2 + -4x + 6 = 0) for verification that your coefficients were entered correctly.
Type: Identifies the equation as Linear, Quadratic (2 real roots), Quadratic (double real root), or Quadratic (complex roots) — describing the nature of the solution before showing the values.
Discriminant (Δ): For quadratic equations, Δ = b² − 4ac. If Δ > 0: two distinct real roots. If Δ = 0: one repeated real root. If Δ < 0: two complex conjugate roots. The discriminant is shown numerically so you can verify the calculation.
Roots: The actual solution value(s). For linear equations: one x value. For quadratics: x1 and x2 (which may be real or complex). Complex roots are displayed in standard a ± bi notation.

Tips for Getting the Best Results

A few techniques help you use the solver efficiently across different equation types and use cases.

Rearrange equations to standard form first: The solver requires coefficients in the form ax + b = 0 or ax² + bx + c = 0. If your equation is not in standard form (e.g., 3x + 7 = 2x − 4), rearrange it first: 3x − 2x = −4 − 7 → x − 11 = 0, so a=1, b=−11.
Use decimal coefficients freely: All three coefficient fields accept any finite decimal number — you don't need to convert fractions to integers. Enter a=1.5, b=−2.3, c=0.7 directly and the solver handles the arithmetic precisely.
Check the discriminant to understand root type before looking at roots: For quadratics, the discriminant immediately tells you whether solutions are real or complex. If you're working on a problem where you expect real solutions, a negative discriminant signals a coefficient entry error worth checking.
For linear equations, make sure a ≠ 0: If a=0, the equation becomes 0·x + b = 0, which either has infinite solutions (if b=0, identity) or no solution (if b≠0, contradiction). The solver identifies both cases correctly, but if you're trying to solve a linear equation, a non-zero a is required.
Use Copy Result for homework or documentation: The Copy Result button copies the full result block including the equation, type, discriminant, and roots as formatted text. This is useful for pasting into homework submissions, notes, or reports without manually transcribing the values.

Why Use an Equation Solver Online

A browser-based equation solver works instantly without a graphing calculator, computer algebra system subscription, or Python environment. It handles the most common equation types that arise in algebra, physics, and engineering coursework. Since all computation happens in the browser, there is no login required and results are private — nothing is sent to any server.

High school and university students use it to check worked solutions before submitting homework. Teachers use it during lesson preparation to verify example problems and generate illustrative examples with specific root properties. Engineers and scientists working with physical formulas that reduce to linear or quadratic equations use it for quick sanity checks without switching to a full CAS. Anyone who encounters the quadratic formula in a practical context — from projectile motion to circuit design to financial break-even analysis — benefits from immediate, reliable computation.

Frequently Asked Questions about Equation Solver

When the discriminant (b² − 4ac) is negative, the quadratic has no real number solutions. The roots are complex numbers of the form a ± bi, where a is the real part, b is the imaginary part, and i is the imaginary unit (√−1). The tool displays these in standard notation, for example: x1 = 1 + 2i, x2 = 1 − 2i. Complex roots always come in conjugate pairs for real-coefficient equations.

Yes. Enter any decimal value for the coefficients a, b, and c — for example a=1.5, b=−2.3, c=0.7. The solver uses JavaScript's 64-bit floating-point arithmetic, which handles most practical decimal values with high precision. Results near zero are displayed as 0 when the computed value is within 10⁻¹² of zero, which prevents display artifacts from floating-point rounding on "clean" equations.

If a=0 in a quadratic form ax² + bx + c = 0, the x² term vanishes and the equation degenerates to bx + c = 0, which is linear. The solver detects this case and shows the type as "Degenerated to linear" rather than treating it as an error — so you can see what happens and get the linear solution. For a proper quadratic, a must be non-zero.

Not currently. The solver supports linear (degree 1) and quadratic (degree 2) equations only. These cover the vast majority of algebra course requirements and many practical applications. For cubic (degree 3) or higher-degree polynomial equations, you would need a computer algebra system such as Wolfram Alpha, MATLAB, or Python's numpy.roots() function, which can handle arbitrary polynomial degrees.

Yes, completely free. No account, no sign-up, and no usage limits. Solve as many equations as you like. All computation runs in your browser with no server involved, so there are no costs and no data sent anywhere — your coefficient values and results remain entirely on your device.

Simply type a minus sign before the number in the coefficient field. For example, to solve x² − 5x + 6 = 0, enter a=1, b=−5, c=6. The number input fields accept negative values directly — just type the minus sign at the start of the value. You can also use the scroll wheel or arrow keys to decrease a value below zero in most browsers.

The discriminant (Δ = b² − 4ac) is a value computed from the quadratic's coefficients that predicts the type of roots before you compute them. Δ > 0 means two distinct real roots (the parabola crosses the x-axis twice). Δ = 0 means one repeated root (the parabola is tangent to the x-axis). Δ < 0 means two complex roots (the parabola does not cross the x-axis at all). It is a key concept in algebra courses and appears frequently in physics and engineering contexts.

Yes. The equation solver works fully on mobile browsers. The coefficient input fields use numeric keyboard inputs on mobile, making it easy to enter values by touch. The equation type buttons, Solve button, and results panel are all accessible on small screens. You can use it on a phone or tablet during a study session or while working through practice problems.