How it works
What this calculadora actually does
The Quadratic Equation Solver works out your quadratic equation calculator in seconds, using the 2026 figures most UK households actually check against.
Quadratic Equation Solver is built to give you a clean, explainable answer without the usual wall of ads — type the numbers, read the result, keep moving.
Getting the arithmetic right first time saves a re-do on paper. Write the formula at the top of the page — then crunch the numbers and the rest of this page explains what the answer means.
Solve any ax² + bx + c = 0 equation. The discriminant (b² − 4ac) tells you how many real roots you have.
On this page you will see Mathematics, BBC Bitesize and MathsIsFun treated as first-class terms — each one is linked to the calculators and references that use it, so you can follow the thread without retyping queries into a search bar.
The formula we run is x = (−b ± √(b² − 4ac)) / 2a. You'll see each term laid out in the worked example below.
If it helps, jump straight to the Maths hub or compare with the Pythagoras Theorem Calculator and the Factorial Calculator — those two calcs are the ones readers usually open right after this page.
A sample run with everything shown
The quickest way to sanity-check any formula is to try it on figures you recognise. Try these:
Solve x² − 5x + 6 = 0: discriminant = 25 − 24 = 1, so x = (5 ± 1) / 2 → x = 3 or x = 2. Sanity check: 3 × 2 = 6 ✓ and 3 + 2 = 5 ✓.
Solve 2x² + 4x + 5 = 0: discriminant = 16 − 40 = −24 < 0, so no real roots. Two complex roots: x = −1 ± i√6/2. In a physics problem this usually means the scenario (a projectile clearing a wall) is impossible with those inputs.
Every run comes back to x = (−b ± √(b² − 4ac)) / 2a — change the inputs, the structure of the answer stays.
Moments this tool earns its keep
Quadratic Equation Solver is aimed at people arriving with questions like these:
- "Quadratic formula"
- "Discriminant formula"
- "Bhaskara formula"
- "What is quadratic equation calculator"
- "How to calculate quadratic equation calculator"
- "Quadratic equation calculator formula"
Where the number stops being useful
Every tool has an edge where it stops being the right answer. Quadratic Equation Solver is no exception:
- For legally binding tax or medical decisions — cross-check with HMRC, NHS or a qualified professional.
- For very large or very small extremes the rounding error outgrows the useful precision.
- When the underlying rate or threshold has changed since the page was last reviewed — always verify with the primary source.
- When the input you have is already a derived figure (net of something) — feeding it in as "gross" will double-subtract.
Mistakes we see over and over
Every time you crunch the numbers for a new scenario, one of these creeps in — it's worth knowing them ahead of time.
- Misreading the unit in the label — 'per year', 'per month' and 'per day' versions of the same figure differ by 12× or 365×.
- Taking a ratio and multiplying it by the wrong side of the inputs — always write the ratio as A/B with labels before running.
- Trusting a screenshot of someone else’s calculation — rerun it yourself with the same inputs, numbers drift.
- Assuming percentages add up. 10% off then 10% more is not the original price — it is 99% of it.
- Not refreshing the page when thresholds are date-sensitive. If the page was cached yesterday, bank rates may already be yesterday’s.
The sources behind the numbers
Where the maths needs an external authority, we cross-check against:
- BBC Bitesize
- MathsIsFun
Works well alongside
If this question keeps coming up for you, the same cluster of tools usually comes next:
- Pythagoras Theorem Calculator — Find the hypotenuse or a missing side of a right-angled triangle using a² + b² = c².
- Factorial Calculator — Calculate n! for any non-negative integer.
How we keep this accurate
Our calculadoras run on pure, unit-tested functions — the same logic lives in the browser and in the CI test suite. When tax rates, thresholds or official figures move, the update lands within 24 hours of the announcement. You can read the editorial policy and corrections policy.
Found an out-of-date number on Quadratic Equation Solver or anywhere else in the Maths toolkit? Send it to the editorial desk and we'll patch it. Or browse the full calculadora directory for the next tool you need.