Quadratic Equation Calculator
Solve ax² + bx + c = 0 from its three coefficients. Read the discriminant and either two real roots or the real and imaginary parts of complex roots.
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Result
Enter the required values to see your result. Use the example to try the complete calculation.
The coefficient a must be nonzero. A negative discriminant means complex roots, not a failed calculation. Displayed roots are numerical approximations.
How this calculation works
Quadratic Equation Calculator
Solve ax² + bx + c = 0 from its three coefficients. Read the discriminant and either two real roots or the real and imaginary parts of complex roots.
Units and limits
The coefficient a must be nonzero. A negative discriminant means complex roots, not a failed calculation. Displayed roots are numerical approximations.
Formulas
- Calculation
- Δ = b² − 4ac; x = (−b ± √Δ) / (2a)
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Discover VISU LinkHow to use it
- Choose the operation when available and enter your own values in the labelled fields.
- Check the units and the limits explained below before interpreting the answer.
- Read the result and its details. Copy it or download a result card; no account is required.
Examples
Worked example
With a=1, b=-3 and c=2, Δ=1 and the roots are 1 and 2.
Another case
With a=1, b=0 and c=1, Δ=-4 and the roots are 0 ± 1i.
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Questions
What does this tool calculate?
Solve ax² + bx + c = 0 from its three coefficients. Read the discriminant and either two real roots or the real and imaginary parts of complex roots.
Which inputs and units should I use?
The coefficient a must be nonzero. A negative discriminant means complex roots, not a failed calculation. Displayed roots are numerical approximations.
Can I check a worked example?
With a=1, b=-3 and c=2, Δ=1 and the roots are 1 and 2.
Are my input values uploaded or stored?
No. The calculation runs in this browser. Typed values are not sent to analytics, placed in the page URL or saved by the calculator. Copying or downloading is an action you choose.
Do I need an account or a paid plan?
No. The calculation, example, result copy and result card are available without registration. VISU services are an optional next step.