Quadratic Solver
Solve ax² + bx + c = 0 with the quadratic formula — every step shown and explained, including the discriminant and simplified radicals.
x² − 5x + 6 = 0
- 1
Identify a, b, and c.
a = 1, b = -5, c = 6
- 2
Compute the discriminant, b² − 4ac.
D = (-5)² − 4(1)(6)
D = 25 − 24 = 1
- 3
Write the quadratic formula and substitute.
x = ( −b ± √D ) / 2a
x = ( 5 ± √1 ) / 2
- 4
√D is a whole number, so simplify each root.
√1 = 1
x = ( 5 + 1 ) / 2 = 3
x = ( 5 − 1 ) / 2 = 2
Solution
x = 3 or x = 2