Solve ax² + bx + c = 0. Find roots, discriminant, and vertex.
Quadratic Equation Solver
Quadratic Equation Solver
ax² + bx + c = 0
About this calculator
What is the Quadratic Equation Solver?
Quadratic Equation Solver solve ax² + bx + c = 0. find roots, discriminant, and vertex. It is part of Home of Calculators's Math Calculators suite for mathematical calculations, equations, formulas. The calculator is designed for students, engineers, scientists, but anyone can use it. No signup, no ads, no tracking. Just accurate math, computed locally in your browser using a BigNumber-precision math engine.
Formula Reference
The Formula
x = (−b ± √(b² − 4ac)) / 2a
The quadratic formula solves any equation of the form ax² + bx + c = 0. The discriminant (b² − 4ac) determines the nature of the roots: positive means two real roots, zero means one repeated root, and negative means two complex roots.
Variables
aCoefficient of x²bCoefficient of xcConstant termWorked Example
a = 1b = -5c = 6
Result: x = 3 or x = 2
How to use the Quadratic Equation Solver
- 1
Identify coefficients
Write the equation in standard form ax² + bx + c = 0 and identify a, b, and c.
- 2
Calculate the discriminant
Compute Δ = b² − 4ac to determine the number and type of roots.
- 3
Apply the formula
Substitute into x = (−b ± √Δ) / 2a to find both roots.
Quick tips
- All calculations run locally in your browser; your data never leaves your device.
- For best results on mobile, rotate to landscape when entering many values.
- Bookmark this page to come back to your calculation anytime.
- Need a different calculator? Try our visual builder to create your own.
Why Home of Calculators
- 100% private (calculations run in your browser)
- 128-bit BigNumber precision (no rounding errors)
- Works on any device: phone, tablet, desktop
- Free forever (no signup, no ads, no upsells)
Frequently asked questions
Is the Quadratic accurate?
+
Yes. Home of Calculators uses a BigNumber-precision math engine (64-128 decimal digits) to ensure calculations are accurate. We run 96+ automated tests covering unit conversion, financial formulas, health formulas, and more. For critical decisions (financial, medical, legal), we still recommend consulting a qualified professional.
Is the Quadratic Equation Solver free?
+
Yes. Every calculator on Home of Calculators is 100% free, with no signup, no ads, and no hidden fees. The entire platform is free forever.
Do you store the values I enter?
+
No. All calculations happen in your browser. We never see, store, or transmit your inputs to any server. Your data stays on your device.
Can I use the Quadratic on my phone?
+
Yes. Home of Calculators is fully responsive and works on any device (phone, tablet, laptop, or desktop). The interface adapts to your screen size.
Can I embed this calculator on my own website?
+
Yes. Click the "Share" button to get an iframe embed code. The embedded calculator will look like any other Home of Calculators widget. You can also build a fully customized version using our visual builder.
Can I build my own custom calculator?
+
Absolutely. Home of Calculators's visual builder lets you add fields, write formulas, choose a theme, and brand the result with your own logo, all without writing code.