Quadratic Equation Solver

Solve quadratic equations with real or complex roots, including linear special cases.

Coefficient aCoefficient bCoefficient c

Solution: x1 = 1
Additional result: x2 = 2

Results update as you type and are rounded to 12 significant digits. Calculations run in your browser.

How it works

Enter a, b, and c for ax² + bx + c = 0. The quadratic formula is x = (−b ± √(b² − 4ac)) / (2a). A positive discriminant gives two real roots, zero gives a repeated root, and a negative discriminant gives complex roots. If a is zero, the solver handles the remaining linear equation. For example, x² − 3x + 2 = 0 has roots 1 and 2.