Linear and quadratic equation solver
Solve a linear equation Bx + C = 0 or a quadratic Ax² + Bx + C = 0 from its coefficients; 2x − 6 = 0 gives x = 3.
- Runs in your browser
- No upload
- Instant result
Assumptions & formula
Formula and assumptions
Bx+C=0; Ax²+Bx+C=0; x=(−B±√(B²−4AC))/(2A)
Coefficients are normalized by the displayed scale before evaluating roots. The original discriminant equals the normalized discriminant times scale squared. A nonzero original discriminant below the decimal range is shown as a scaled expression, never as zero.
Results
Enter values and press Calculate to see the result here.
How to use this calculator
- Set inputs and units
Choose linear or quadratic mode and enter the coefficients of ax²+bx+c=0, including signs and a constant term of zero.
- Calculate
Check this worked example: linear: b=2, c=-6 → 2x−6=0 → x=3
- Results
Substitute each root that is returned back into the original equation. No solution and infinitely many solutions are different outcomes.
Questions and limits
Can I paste an arbitrary equation?
No. Rearrange it into coefficient form yourself. Linear mode uses b and c, not free-form expressions or systems of equations.
Which input errors should I correct?
Move every term to the left side and keep the minus signs. The numeric fields accept decimal points but not an equals sign.
What does this calculation leave out?
Only one linear or quadratic polynomial is solved. Higher-degree equations, inequalities and multivariable systems are not supported.