Quadratic Formula — How to Solve Quadratic Equations
The quadratic formula solves any equation of the form ax² + bx + c = 0, giving you the exact values of x (roots of the equation).
Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a
Where:
- a = Coefficient of x²
- b = Coefficient of x
- c = Constant term
- x = Unknown variable (solution)
Step-by-Step:
- 1
Identify a, b, c
From the equation ax² + bx + c = 0.
- 2
Calculate discriminant
D = b² - 4ac. If D > 0: two real roots. D = 0: one root. D < 0: no real roots.
- 3
Apply formula
x = (-b ± √D) / 2a.
Worked Examples:
x² - 5x + 6 = 0
a: 1b: -5c: 6
Result: x = 3 or x = 2
D = 25-24 = 1. x = (5±1)/2 → x = 3 or x = 2