Quadratic Equation Solver

Solve ax^2 + bx + c = 0 with discriminant analysis, exact radical and complex roots, step-by-step work, vertex/factored forms, and visual parabola graph.

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Quadratic Equation Solver

Solve ax² + bx + c = 0 with discriminant analysis, exact radical roots, complex solutions, step-by-step work, vertex and factored forms, and a visual parabola graph.

Coefficients

ax² + bx + c = 0

Solution
Two real roots

Equation
x² − 5x + 6 = 0
Discriminant Δ
1
Parabola opens
up
Root 1 (decimal)
3
Root 2 (decimal)
2
Factored Form
(x − 3)(x − 2)
Vertex Form
(x − 2.5)² − 0.25

Frequently Asked Questions

What does the discriminant tell me?

Delta = b^2 - 4ac. Delta > 0: two real roots; Delta = 0: one repeated real root; Delta < 0: complex conjugate pair.

Why show decimal AND radical forms?

Decimal is convenient for follow-up calculations, but simplified radical form ((3 + sqrt(5))/2) is exact and often required in algebra classes.

How do I read the graph?

The vertex (-b/2a, c - b^2/4a) is marked amber; real roots green; y-intercept red — all key features at a glance.

Is the Quadratic Equation Solver free to use?

Yes, the Quadratic Equation Solver is 100% free with no registration, no hidden fees, and no usage limits. All processing happens locally in your browser, ensuring complete privacy.

Is my data safe with this tool?

Absolutely. The Quadratic Equation Solver processes everything client-side in your browser. No data is uploaded to or stored on any server. Your content remains private on your device at all times.

Does the Quadratic Equation Solver work on mobile devices?

Yes, the Quadratic Equation Solver is fully responsive and works on smartphones and tablets. You can use it on any device with a modern web browser -- no app download required.

Do I need to create an account to use this tool?

No account or registration is needed. Simply open the Quadratic Equation Solver in your browser and start using it immediately. There are no sign-up walls or usage restrictions.

How accurate are the calculations?

The Quadratic Equation Solver uses industry-standard formulas and algorithms to ensure accurate results. However, for critical financial or medical decisions, always consult a qualified professional.

Which browsers are supported?

The Quadratic Equation Solver works in all modern browsers including Chrome, Firefox, Safari, Edge, and Opera. For the best experience, use the latest version of your preferred browser.

About Quadratic Equation Solver

Quadratic Equation Solver is a free, browser-based tool in our Calculator Tools collection. Everything runs locally on your device — no uploads, no sign-up, and your data stays private.

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