Quadratic Equation Solver
Free quadratic equation solver. Solve ax² + bx + c = 0 instantly for real and complex roots, discriminant, and vertex, with step-by-step working and a parabola graph.
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What is Quadratic Equation Solver?
The Quadratic Equation Solver is a free, browser-based tool that solves any equation of the form ax² + bx + c = 0 using the quadratic formula x = (−b ± √Δ) / (2a). It computes the discriminant Δ = b² − 4ac to classify the roots — two distinct real roots, one repeated real root, or two complex conjugate roots — and also returns the vertex and axis of symmetry of the parabola. Every step of the working is shown, and an interactive parabola graph highlights the vertex and x-intercepts. All math runs locally in your browser, so results are instant and your inputs never leave your device.
Key Benefits
- Solves every case: two real roots, one repeated root, or two complex roots
- Shows the discriminant and explains what it means for the roots
- Computes the vertex and direction of opening of the parabola
- Step-by-step working is ideal for checking algebra homework
- 100% client-side — instant results, fully private, no sign-up
Common Use Cases
- •Checking homework answers in algebra and precalculus classes
- •Finding the x-intercepts (roots) of a parabola for graphing
- •Solving physics problems involving projectile motion (free fall)
- •Calculating break-even points and profit-maximization in business math
- •Engineering problems that reduce to a second-degree equation
How to Use the Quadratic Equation Solver
- Enter the coefficients: Type the values of a (the x² coefficient), b (the x coefficient), and c (the constant term) into the three input boxes. Decimals and negative numbers are supported.
- Read the roots: The solver immediately displays the roots. Depending on the discriminant, you will see two distinct real roots, one repeated real root, or two complex conjugate roots.
- Check the discriminant and vertex: Review Δ = b² − 4ac to understand the nature of the roots, and the vertex to see the minimum or maximum point of the parabola.
- Copy or study the steps: Use Copy to save the full solution, or follow the step-by-step working and parabola graph to learn how the answer was found.
Key Features
- Solves ax² + bx + c = 0 using the quadratic formula x = (−b ± √Δ) / (2a) for any real coefficients
- Automatically classifies roots via the discriminant Δ = b² − 4ac: two real, one repeated real, or two complex conjugates
- Handles edge cases gracefully, including degenerate linear equations (a = 0) and constant equations (a = b = 0)
- Computes the vertex and axis of symmetry, and shows whether the parabola opens upward or downward
- Plots an interactive parabola graph with the vertex and x-intercepts clearly marked
- Provides full step-by-step working, perfect for checking algebra homework and learning the quadratic formula