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Quadratic Equation Solver

Solve ax² + bx + c = 0 with real, repeated, and complex roots, discriminant analysis, and parabola vertex.

Solve ax² + bx + c = 0 with real, repeated, or complex roots & vertex

Coefficient a

Coefficient b

Coefficient c

Roots of 1x² + (-5)x + (6) = 0

Root x₁

3.0000

Root x₂

2.0000

Discriminant (Δ): 1Parabola Vertex (h, k): (2.50, -0.25)

Equation: 1x² + (-5)x + (6) = 0

Step 1: Compute discriminant Δ = b² - 4ac = (-5)² - 4(1)(6) = 1

Step 2: Since Δ > 0, there are two distinct real roots.

x₁ = (-b + √Δ) / 2a = (-(-5) + 1.0000) / 2 = 3.0000

x₂ = (-b - √Δ) / 2a = (-(-5) - 1.0000) / 2 = 2.0000

How to Use Quadratic Equation Solver

Enter a, b, and c coefficients.

Examine Δ = b² - 4ac to determine root character.

Get real roots or complex conjugates with full derivations.

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