Quadratic equation calculator
Enter a, b and c to solve ax² + bx + c = 0.
Quadratic equation calculator
Solve any quadratic equation ax² + bx + c = 0 for its roots, real or complex, and see the discriminant. Just enter the coefficients a, b and c.
The quadratic formula
x = (−b ± √(b² − 4ac)) / 2a. The discriminant Δ = b² − 4ac tells you the nature of the roots: Δ > 0 gives two real roots, Δ = 0 gives one repeated root, and Δ < 0 gives two complex conjugate roots. If a = 0 the equation is linear and is solved as bx + c = 0.
Frequently asked questions
What is the discriminant? Δ = b² − 4ac; its sign tells you whether the roots are real or complex.
What if there are no real roots? The calculator shows the complex roots in the form p ± qi.