Quadratic Formula Calculator
Solve ax² + bx + c = 0. Real or complex roots, with the discriminant shown.
The quadratic formula
x = (-b ± √(b² - 4ac)) / 2a
The expression under the root, b² - 4ac, is the discriminant, and it tells you what kind of roots to expect before you solve anything: positive means two distinct real roots, zero means one repeated root, negative means a complex conjugate pair.
Worked example
x² - 3x + 2 = 0: the discriminant is 9 - 8 = 1, so √1 = 1 and x = (3 ± 1) / 2, giving x₁ = 2 and x₂ = 1. Check by factoring: (x - 1)(x - 2) = 0.