📐

Equation Solver

Solve linear and quadratic equations quickly. Supports real and complex roots for quadratic equations.

Result

Equation
—
Type
—
Discriminant
—
Roots
—

About Equation Solver

This tool solves linear and quadratic equations in standard algebraic form. Linear equations have one variable term, while quadratic equations include a squared term and may produce two real or two complex roots.

Supported Forms

  • Linear: ax + b = 0 — one real solution
  • Quadratic: ax² + bx + c = 0 — up to two solutions (real or complex)

How to Use

  1. Choose Linear or Quadratic from the equation type selector.
  2. Enter the coefficients a, b, and (for quadratic) c.
  3. Click Solve — the solution(s) and step-by-step working appear below.

How It Works

For linear equations: x = −b / a.
For quadratic equations: the discriminant Δ = b² − 4ac determines the nature of roots. If Δ > 0, two distinct real roots. If Δ = 0, one repeated root. If Δ < 0, two complex conjugate roots.

Example

Solve 2x² − 4x − 6 = 0: a=2, b=−4, c=−6. Discriminant = 16 + 48 = 64. Roots: x = (4 ± 8) / 4 → x = 3 and x = −1.

Frequently Asked Questions

When the discriminant is negative, the quadratic has no real solutions. The roots are complex numbers of the form a ± bi, where i is the imaginary unit (√−1). The tool displays these clearly.
Yes. Enter decimal values for any coefficient (e.g. a=1.5, b=−2.3, c=0.7). The solver handles both integer and floating-point inputs.
If a=0, the equation becomes linear (not quadratic). Use the Linear equation type instead, or enter a non-zero value for a.
Not currently. The solver supports linear (degree 1) and quadratic (degree 2) equations only. For higher-degree polynomials, consider using a computer algebra system.