Quadratic Equation Solver

Solve ax² + bx + c = 0 and inspect the discriminant.

InputsChange a value to recalculate instantly

ResultUpdates as you type

Discriminant (Δ)1

Rootsx₁ = 3, x₂ = 2

FORMULA & STEPSQuadratic Equation Solver — Mathematical Derivation & Steps

4 StepsSequential Calculation Breakdown

Identify Coefficients

Standard quadratic equation: (1)x^2 + (-5)x + (6) = 0.

Calculate Discriminant (Δ)

Because Δ > 0, there are two distinct real roots.

Substitute into Quadratic Formula

Apply algebraic simplification.

Final Solutions

Verified intersection points where the parabola crosses y = 0.

λ DooMathWork with this calculation

Local · deterministic · optional

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Quick mathNatural-language-style shortcuts for deterministic arithmetic.

Calculator guide

How to use the Quadratic Equation Solver

Solve ax² + bx + c = 0 and inspect the discriminant.

01Set inputsChoose values, units and assumptions.

02Apply the modelUse the stated mathematical relationship.

03Read the resultCheck the output against the assumptions before using it.

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Solve ax² + bx + c = 0 and inspect the discriminant.

functions

The result is calculated from the inputs and assumptions shown in the calculator.

fact_check

Review the inputs, units and assumptions before using the result for a real decision.