Quadratic Formula Solver

Solve ax² + bx + c = 0 using the quadratic formula. Get real and complex roots with full step-by-step working and discriminant analysis.

x = (−b ± √(b²−4ac)) / 2a

Quick Examples

a (x² coeff)

b (x coeff)

c (constant)

Step-by-step solution

The Quadratic Formula

For ax² + bx + c = 0, the solutions are x = (−b ± √(b²−4ac)) / 2a. The discriminant Δ = b²−4ac determines the nature of the roots: Δ>0 means two distinct real roots; Δ=0 one repeated root; Δ<0 two complex (imaginary) roots.