Quadratic Equation Solver
Solve ax² + bx + c = 0 with full step-by-step working.
Enter coefficients for ax² + bx + c = 0
1x² − 5x + 6 = 0
Discriminant (b²−4ac)1
Root typetwo real roots
Vertex (h, k)(2.5, -0.25)
Axis of symmetryx = 2.5
x = 3
x = 2
Step-by-step
1. Discriminant = b² − 4ac = (-5)² − 4·(1)·(6) = 1
2. √discriminant = 1
3. x = (−b ± √discriminant) / 2a = (−(-5) ± 1) / 2
Quadratic Formula
Any equation of the form ax² + bx + c = 0 (where a ≠ 0) is solved with the quadratic formula: x = (−b ± √(b²−4ac)) / 2a. The discriminant (b²−4ac) determines the nature of roots: positive → two real roots, zero → one repeated root, negative → two complex roots.
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