What is a Quadratic Equation Solver?
A quadratic equation solver instantly finds the solutions (roots) to any equation in the form axยฒ + bx + c = 0. It applies the quadratic formula and tells you whether you have two real roots, one repeated root, or two complex roots.
Students use it to check homework, while professionals in engineering, physics, and finance use it to quickly solve equations that arise in real-world modeling. No more trial-and-error โ just enter your coefficients and get instant, accurate answers.
How to Use the Quadratic Solver
Step 1: Enter Coefficient a
Input the coefficient of xยฒ (the number in front of xยฒ). Example: 1
Step 2: Enter Coefficient b
Input the coefficient of x (the number in front of x). Example: -5
Step 3: Enter Coefficient c
Input the constant (the plain number with no x). Example: 6
Step 4: See Both Roots
The solver shows xโ and xโ, plus the discriminant โ which tells you what type of roots you have.
Understanding the Discriminant
| Discriminant (ฮ = bยฒ โ 4ac) | Result |
|---|---|
| ฮ > 0 | Two distinct real roots |
| ฮ = 0 | One repeated real root |
| ฮ < 0 | Two complex conjugate roots |
Why Use Our Quadratic Solver?
๐ข Real & Complex Roots
Handles all cases โ positive, zero, or negative discriminant โ including imaginary number results.
๐ Discriminant Shown
See the discriminant value and what it tells you about the nature of the roots.
๐ฏ Decimal Coefficients
Works with decimal or negative coefficients, not just whole numbers.
โก Instant Results
No forms, no ads getting in the way, no waiting. Get your answer immediately.
๐ฑ Mobile Friendly
Works perfectly on phones, tablets, and desktop โ calculate on the go.
๐ 100% Free
No subscriptions, no sign-ups, no hidden fees. Use it as many times as you need.
Frequently Asked Questions
The discriminant (ฮ) is bยฒ โ 4ac. If it is positive, you get two real roots. If it is zero, you get one repeated root. If it is negative, you get two complex roots.
When the discriminant is negative, the roots involve "i" (the imaginary unit, where iยฒ = โ1). Complex roots always come in conjugate pairs, such as 2 + 3i and 2 โ 3i.
Graphing shows you visually where the parabola crosses the x-axis. This calculator gives you the exact numerical values of the roots instantly.
Yes โ enter decimal numbers such as 0.5 or 3.14 and the solver handles them perfectly.
If a = 0, the equation is no longer quadratic (it becomes linear). The calculator requires a non-zero value for a.
Ready to Solve Your Equation?
Use our free quadratic equation solver now. No sign-up required, results in seconds.
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