How to use Quadratic Equation Solver
- Enter the coefficients a, b and c from the equation.
- Leave the decimal places at 4, or pick another precision.
- Read the discriminant and the nature of the roots first.
- Check each root against the substitution steps under the answer.
Example: Quadratic Equation Solver
Solve x² - 3x + 2 = 0 and check both roots.
Options
- Coefficient a
- The number in front of x². Enter 0 and the page solves the linear equation instead, without a discriminant.
- Coefficient b
- The number in front of x. A sign in front of the term belongs to the coefficient, so -3x is entered as -3.
- Constant c
- The term with no x in it. Enter 0 when the equation has no constant term.
- Decimal places
- 0, 2, 4, 6 or 8 places. The discriminant stays exact, and the answer states when a root had to be rounded.
Supported inputs and limits
Where your input is processed
This tool processes your input in this browser. Your text and files are not uploaded to UseFreeTools. Check this tool's limits for anything it may save on your device.
Why the discriminant is worth reading first
The quadratic formula x = (-b ± √D) ÷ (2a) only produces a real number when the discriminant under the square root is zero or positive. A negative discriminant means that square root has no real value, so the two solutions are a complex conjugate pair and the parabola never meets the x axis. Reading D first tells you which of those three cases you are in before any division happens.
Decimal coefficients and exact arithmetic
Binary floating point cannot hold 0.1 exactly, so a solver built on doubles can report 0.09999999998 where the answer should be 0.1, and a discriminant of zero can drift just above it. This page works in decimal arithmetic instead: the coefficients you type are the coefficients it uses, so a repeated root stays a repeated root.
Questions about Quadratic Equation Solver
What does the discriminant tell me?
Its sign decides the roots. A positive discriminant gives two distinct real roots, zero gives one repeated real root, and a negative discriminant gives a complex conjugate pair because the square root has no real value.
What happens when coefficient a is 0?
The x² term disappears and the page solves the linear equation bx + c = 0. There is no discriminant to report, and a single root comes back unless b is also 0.
Why does it say the roots were rounded?
A root such as 2 ÷ 3 has no exact decimal form. The page shows it at your chosen precision and labels that as rounded, while an exact root such as 1 stays plain.
Is the equation rearranged for me?
No. Move every term to the left side first. The equation 2x² = 8 becomes 2x² - 8 = 0, and its coefficients are then a = 2, b = 0 and c = -8.
How do I check a root by hand?
Put the root back into the original equation. The substitution steps use the coefficients you entered, so x = 2 in x² - 3x + 2 gives 4 - 6 + 2, which is 0.