Quadratic Formula Calculator
Enter the coefficients a, b and c to solve ax² + bx + c = 0. You get both roots, the discriminant, and the complex roots when the parabola never crosses zero. The working is shown line by line. A free quadratic formula calculator that runs in your browser.
- Exact, step-by-step answers
- 100% free
- No sign-up, no app
- Instant as you type
- Works offline after first load
For the equation a·x² + b·x + c = 0.
Two distinct real roots.
How to use it
- 1
Enter a, b and c
Type the three coefficients from your equation in the form ax² + bx + c = 0. The value of a cannot be zero, since that makes the equation linear.
- 2
Read the discriminant
The calculator shows b² − 4ac first, because its sign tells you whether the roots are two real, one repeated, or a complex pair.
- 3
Read both roots
See x₁ and x₂ worked out from the formula, in exact form where it is clean and as decimals otherwise.
When it comes in handy
Algebra homework
Solve a quadratic and check your roots against the discriminant so you understand why there are two answers, one, or none on the real line.
Physics and projectiles
Find when a height or distance reaches zero, which is a quadratic in time for anything thrown or dropped.
Checking by hand
Confirm a result you got with the formula yourself, including the complex case where sign mistakes are common.
Instant, exact & 100% in your browser
The maths runs right here in your browser, with fractions and whole numbers kept exact rather than rounded along the way. Nothing you type is sent to a server, there is no sign-up and no limit, and once the page has loaded it keeps working even with no connection.
Frequently asked questions
- What is the quadratic formula?
- It is x = (−b ± √(b² − 4ac)) ÷ 2a, and it gives both roots of any equation written as ax² + bx + c = 0. The ± sign is why a quadratic usually has two solutions. This calculator fills in your a, b and c and shows each step.
- What does the discriminant tell me?
- The discriminant is b² − 4ac. If it is positive there are two different real roots, if it is zero there is one repeated real root, and if it is negative the two roots are a complex conjugate pair. The calculator labels which case you are in.
- Can it give complex roots?
- Yes. When the discriminant is negative the equation has no real roots, but it does have two complex roots like −1 + 2i and −1 − 2i. The calculator works these out instead of just reporting no solution.
- Does this work offline and is anything sent to a server?
- The calculation runs entirely in your browser, so nothing you type is sent anywhere, and once the page has loaded it keeps working with no connection. There is no sign-up and no limit on how many calculations you make.
More tools
More from the Hivly network
Free sister tools on our other sites.