Quadratic Equation Solver

The Quadratic Formula

The Formula

x = (−b ± √(b²−4ac)) ÷ 2a. The ± gives two solutions (roots). When the discriminant (b²−4ac) is positive: two real roots. When zero: one repeated root. When negative: two complex roots.

Example

For x² − 5x + 6 = 0: a=1, b=−5, c=6. Discriminant = 25 − 24 = 1. Roots = (5 ± 1) ÷ 2 = 3 and 2.

Applications

Quadratic equations model projectile motion, area problems, profit maximisation, and countless physics problems. The roots represent where the parabola y = ax² + bx + c crosses the x-axis.