Explanation

The quadratic formula solves ax² + bx + c = 0: x = (-b ± √(b²-4ac)) / 2a. It works for any quadratic equation, unlike factoring which only works when solutions are nice numbers.

Steps: identify a, b, c coefficients, calculate discriminant (b²-4ac), substitute into formula. The ± gives two solutions (where the parabola crosses the x-axis).

Discriminant tells solution type: positive = two real solutions, zero = one repeated solution, negative = no real solutions (complex numbers). Always check solutions by substituting back.