Equation Solver

Linear and quadratic equations with real solutions

Quick Answer

Equation Solver: Linear and quadratic equations with real solutions. Equation Solver uses standard math formulas to compute accurate results instantly.

a·x² + b·x + c = 0

x₁ = 2.0000 · x₂ = 1.0000

x₁2.000000

x₂1.000000

Discriminant Δ1.0000

Vertex (x, y)(1.5000, -0.2500)

Axis of symmetryx = 1.5000

Solution steps

1Δ = b² − 4ac = -3.0000² − 4×1.0000×2.0000 = 1.0000 > 0
2Two distinct real roots:
3x = (−b ± √Δ) / 2a = (3.0000 ± 1.0000) / 2.0000
4x₁ = 2.000000 · x₂ = 1.000000
5Sum of roots = −b/a = 3.0000 · product = c/a = 2.0000 (Vieta)

Formulas

Linear: x = −b/a. Quadratic: x = (−b ± √(b²−4ac))/2a; Δ > 0 two roots, Δ = 0 repeated, Δ < 0 complex pair. 2×2 system: Cramer's rule x = (ed−bf)/D, y = (af−ec)/D with D = ad−bc.

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How to Use

Enter values or expressions: type directly into the Equation Solver — keyboard friendly.
Instant results: everything computes live as you type, no button needed.
Follow the steps: the result panel shows full working and formula substitution.
Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

Equation Solver is a free online math tool — open and use, no sign-up.
All calculations run locally in your browser; your data never leaves the device.
Key capability: Linear and quadratic equations with real solutions.
Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Equation Solver formula

Equation Solver uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Equation Solver?

Open the page and fill in the input fields — results update automatically. Linear and quadratic equations with real solutions.

Are the results accurate?

Yes. All calculations use standard mathematical formulas and are verified for accuracy.

Is it free? Do I need to sign up?

Completely free. No registration, login or download required — just open and use.

Does it work on mobile?

Yes. The responsive design works on phones, tablets and desktops.

Is my data saved?

No. All calculations run locally in your browser. Nothing is uploaded or stored.

Related Guides

Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated: 2026-08-03

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Cite this page: YiJianSuan. Equation Solver[EB/OL]. https://www.yijiansuan.com/en/c/math/equation

Results provided by this tool are for reference only and do not constitute professional advice.