Quadratic Equation Solver

For ax² + bx + c = 0:
x = (−b ± √(b² − 4ac)) / (2a)
The expression b² − 4ac is the discriminant. If D > 0: two distinct real roots. D = 0: one repeated root. D < 0: two complex (imaginary) roots.

D = b² − 4ac tells you the nature of the roots before you solve. D > 0 → two real, distinct roots (the parabola crosses the x-axis twice). D = 0 → one repeated real root (the parabola just touches the x-axis). D < 0 → no real roots; two complex conjugate roots.

Find two numbers that multiply to a×c and add to b. Example: x²+5x+6 → a×c = 6, b = 5 → 2 and 3 → (x+2)(x+3) = 0 → x = −2 or x = −3. For equations that don't factorise neatly, the quadratic formula always works.