Equation Solver
Solve linear and quadratic equations, systems of two linear equations and proportions, with discriminants and exact fractions.
How to Use
- Choose a type
Pick linear, quadratic, system or proportion from the dropdown and the matching coefficient fields appear.
- Enter coefficients
Type the coefficients (decimals and negatives allowed) and the solution updates live.
- Read the result
The discriminant or a note appears beside the solution; fractions are reduced and decimals keep 10 significant digits.
FAQ
Why are results shown as both a fraction and a decimal?
Many roots are repeating decimals (e.g. 2/3), which look suspicious when printed as decimals alone. The tool finds the approximate root with floating point and then recovers the simplest fraction via a continued-fraction algorithm (denominator capped at one million), showing both — exact and readable.
What does the discriminant mean?
For ax² + bx + c = 0 the discriminant is Δ = b² − 4ac. Δ > 0 means the parabola crosses the x-axis twice (two distinct real roots); Δ = 0 means it touches once (one repeated root); Δ < 0 means no crossing (no real roots, two complex conjugates).
When does a system have no solution?
When the determinant D = a₁b₂ − a₂b₁ is zero, the two lines are either parallel (no solution) or coincident (infinitely many). The tool reports the absence of a unique solution; check whether the two equations are proportional.
What if a = 0?
For a linear equation a = 0 degenerates to comparing constants; for a quadratic it degenerates to a linear equation. The tool explains both cases instead of returning a misleading solution.