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Key Features
Instant Calculation
Get accurate results in real time with our optimized algorithm.
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100% Free
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Every quadratic equation in the form ax² + bx + c = 0 can be solved using the quadratic formula, which always gives the correct roots — whether they're two real numbers, one repeated real number, or a pair of complex numbers.
This solver identifies which case applies from the discriminant and works through the full formula.
How it works
Enter the coefficients a, b, and c from your equation. The calculator computes the discriminant (b² - 4ac) to determine the type of roots, then substitutes into the quadratic formula to find them.
- Enter a (coefficient of x²).
- Enter b (coefficient of x).
- Enter c (constant).
- Click Calculate to see your results.
Examples
A simple factorable equation
x² - 3x + 2 = 0 has a discriminant of 1, giving two real roots: x = 2 and x = 1 — matching the factored form (x-1)(x-2) = 0.
Who should use it
- Solving algebra homework problems step by step.
- Checking work on a quadratic equation by hand.
Industry applications
- Mathematics education
- Engineering and physics (projectile motion, optimization problems)
Advantages
- Handles all three cases: real, repeated, and complex roots.
- Shows the discriminant and full formula substitution.
Common mistakes to avoid
- Forgetting the ± in the quadratic formula, which loses one of the two roots.
- Sign errors when substituting a negative b into the formula (remember it becomes -b, so a negative b becomes positive).
Best practices
- Calculate the discriminant first and check its sign before working through the rest of the formula — it tells you what kind of answer to expect.
Tips
- If you can factor the equation easily by inspection, the quadratic formula will always agree with your factored answer — it's a good way to double-check your work.