The solver accepts positive numbers, negative numbers, decimals, zero for b or c, and scientific notation. It reports complex conjugate roots when the parabola does not cross the x-axis. No equation data is uploaded or stored.
Private browser utility / Calculators
Quadratic Equation Solver
Runs entirely in your browser - no upload, no sign-up.
ax² + bx + c = 0
Enter three coefficientsThe roots, discriminant, vertex, and formula steps will update live.
What does a quadratic equation solver calculate?
A quadratic equation solver finds the two solutions of ax² + bx + c = 0 using the quadratic formula. Enter a, b, and c to see real, repeated, or complex roots, plus the discriminant, vertex, axis of symmetry, and each substitution step. Everything calculates instantly in your browser.
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How to use
- 01Write the standard form
Move every term to the left so the equation reads ax² + bx + c = 0.
- 02Enter the coefficients
Type the numbers multiplying x² and x, followed by the constant term.
- 03Read the working
Review the roots, discriminant, vertex, and formula substitution as they update.
- 04Copy the solution
Copy the complete result to check homework or save your working.
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Who it's for
- Check algebra homework while keeping the formula steps visible.
- Find where a projectile or parabola crosses the x-axis.
- Classify a quadratic by its positive, zero, or negative discriminant.
- Verify the vertex and axis of symmetry before sketching a graph.
FAQ
Is my quadratic equation uploaded?
No. Your coefficients and results stay in your browser. The solver performs the arithmetic locally and does not send the equation to a calculation service.
Is this quadratic equation solver free?
Yes. You can solve as many quadratic equations as you need without an account, payment, or download.
What coefficient limits does the solver have?
It accepts finite JavaScript numbers, including decimals and scientific notation. Extremely large coefficients that overflow browser number arithmetic are rejected with an error instead of showing an unreliable answer.
What happens when the discriminant is negative?
A negative discriminant means the equation has no real roots. The solver returns two complex conjugate roots with the same real part and opposite imaginary parts, such as -2 + 2i and -2 - 2i.
Can a quadratic equation have only one solution?
Yes. When b² - 4ac equals zero, both formula branches give the same value. This repeated root is where the parabola touches the x-axis at its vertex.
Why can coefficient a not equal zero?
If a equals zero, the x² term disappears and the equation becomes linear rather than quadratic. This solver flags that case so it does not apply the quadratic formula incorrectly.
How does the solver find the vertex?
The vertex x-coordinate is -b/(2a), which is also the axis of symmetry. Its y-coordinate can be calculated as -D/(4a), where D is the discriminant.