Rex says
The fast lane for the math you almost remember from school. Type the numbers, get the answer, move on with your day.
Try a scenario
Click to load — tweak from there.Inputs
Result
Roots
x = 3.0000 or 2.0000
Root type
Two distinct real roots
Discriminant (b² − 4ac)
1.0000
Vertex x
2.5000
Vertex y
-0.2500
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One click, a permanent link with your numbers baked in.
How to use this
- 1Enter a (x² coefficient).
- 2Enter b (x coefficient).
- 3Enter c (constant).
- 4Read your roots on the right — it updates as you type.
- 5Hit Share to keep the scenario or send it to someone.
About this calculator
Solves any quadratic using the quadratic formula. The discriminant tells you the shape of the answer before you compute it: positive gives two real roots, zero gives one, negative gives a complex pair.
Worked example
Using the values the calculator loads with:
Inputs
- a (x² coefficient): 1
- b (x coefficient): -5
- c (constant): 6
Results
- Roots: x = 3.0000 or 2.0000
- Root type: Two distinct real roots
- Discriminant (b² − 4ac): 1
- Vertex x: 2.5
- Vertex y: -0.25
What each field means
Inputs
- a (x² coefficient)
- The a (x² coefficient) used in the calculation. Starts at 1 so you have a working example on load.
- b (x coefficient)
- The b (x coefficient) used in the calculation. Starts at -5 so you have a working example on load.
- c (constant)
- The c (constant) used in the calculation. Starts at 6 so you have a working example on load.
Results
- Roots
- Returned as a plain value and shown as the headline result. It recalculates instantly whenever you change an input, so you can compare scenarios without reloading.
- Root type
- Returned as a plain value. It recalculates instantly whenever you change an input, so you can compare scenarios without reloading.
- Discriminant (b² − 4ac)
- Returned as a decimal number. It recalculates instantly whenever you change an input, so you can compare scenarios without reloading.
- Vertex x
- Returned as a decimal number. It recalculates instantly whenever you change an input, so you can compare scenarios without reloading.
- Vertex y
- Returned as a decimal number. It recalculates instantly whenever you change an input, so you can compare scenarios without reloading.
FAQ
How does the quadratic equation solver work?
Solves any quadratic using the quadratic formula. The discriminant tells you the shape of the answer before you compute it: positive gives two real roots, zero gives one, negative gives a complex pair. The underlying maths is: x = (−b ± √(b² − 4ac)) ÷ 2a.
What do I need to enter?
3 values: a (x² coefficient), b (x coefficient), and c (constant). Each field starts with a sensible default, so you can change one number at a time and watch the result move.
What does the roots result mean?
It is returned as a plain value and updates live as you edit the inputs, so you can compare two or three versions of a scenario in a few seconds.
Is this calculator free, and do I need an account?
Yes, it's free, and no account is required. Nothing you type is stored on our servers — the maths runs entirely in your browser.
How accurate is the result?
It applies the standard formula exactly, so the arithmetic is precise. Results are rounded for display; the underlying calculation keeps full precision.
Who is this tool for?
It's built for students, developers, and anyone who needs the answer right now without setting up a spreadsheet.
Accuracy and limitations
- Results are rounded for display; the underlying calculation keeps full precision.
- Very large or very small inputs may hit floating-point limits in the browser.
- Inputs outside the accepted range are clamped rather than rejected.
Related tools
Cite this calculator
Writing about this topic? Grab a citation — every link helps keep these tools free.
RevenueLab. (2026). Quadratic Equation Solver. Retrieved from https://www.revenuelab.fyi/toolbox/quadratic-equation
<p>Source: <a href="https://www.revenuelab.fyi/toolbox/quadratic-equation" target="_blank" rel="noopener">Quadratic Equation Solver — RevenueLab</a> (2026).</p>
Source: [Quadratic Equation Solver — RevenueLab](https://www.revenuelab.fyi/toolbox/quadratic-equation) (2026).