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Quadratic Formula Calculator

Solve ax² + bx + c = 0 — real and complex roots with step-by-step solution

1x² + -5x + 6 = 0

Discriminant (b² − 4ac)

1

Two distinct real roots

Roots

x₁

3

x₂

2

Vertex (turning point)

(2.5, -0.25)

The parabola opens upward ↑

Step-by-step solution

  1. 1Given: 1x² + -5x + 6 = 0
  2. 2Discriminant: b² − 4ac = -5² − 4(1)(6) = 25 − 24 = 1
  3. 3D > 0: two distinct real roots
  4. 4x₁ = (−-5 + √1) / (2×1) = 3.000000
  5. 5x₂ = (−-5 − √1) / (2×1) = 2.000000
  6. 6Vertex: (2.5000, -0.2500)
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