Quadratic Equation Solver
Solve ax² + bx + c = 0 — find roots, discriminant, vertex, and full step-by-step working.
1x² − 5x + 6 = 0
Discriminant (Δ = b² − 4ac)
1
Δ > 0 → Two distinct real roots
Roots — Two Real Roots
x₁
3
x₂
2
Parabola Info
VERTEX
(2.5, -0.25)
OPENS
⌣ Upward (a > 0)
Full Step-by-step Solution
Equation1x² + -5x + 6 = 0
DiscriminantΔ = b² − 4ac = (-5)² − 4(1)(6) = 25 − 24 = 1
Discriminant > 0Two distinct real roots
x₁x₁ = (−b + √Δ) / 2a = (5 + √1) / 2 = (5 + 1) / 2 = 3
x₂x₂ = (−b − √Δ) / 2a = (5 − √1) / 2 = (5 − 1) / 2 = 2
Vertex(−b/2a, c − b²/4a) = (2.5, -0.25)