Equation Solver
Solve linear equations, quadratic equations (including complex roots), and 2×2 systems of linear equations. Step-by-step results make it ideal for checking homework or understanding algebra.
Solve: ax + b = c
Key Formulas
Linear (ax + b = c): x = (c − b) / a
Quadratic (ax² + bx + c = 0):
x = (−b ± √(b² − 4ac)) / 2a
2×2 System (Cramer's Rule):
det = a₁b₂ − a₂b₁
x = (c₁b₂ − c₂b₁) / det
y = (a₁c₂ − a₂c₁) / det
Quadratic Discriminant (Δ = b² − 4ac)
| Δ > 0 | Two distinct real roots |
| Δ = 0 | One repeated real root (double root) |
| Δ < 0 | Two complex conjugate roots (no real solution) |
How to use
Linear equation (ax + b = c)
Enter coefficients a, b, and c. The calculator solves for x. Example: 3x + 5 = 14 → a=3, b=5, c=14 → x=3.
Quadratic equation (ax² + bx + c = 0)
Enter a, b, c. The discriminant (b²−4ac) determines the nature of the roots: positive → two real roots, zero → one repeated root, negative → two complex (imaginary) roots.
2×2 linear system
Solves two simultaneous equations using Cramer's Rule. Enter the coefficients for each equation: a₁x + b₁y = c₁ and a₂x + b₂y = c₂.
Formula
Quadratic: x = (−b ± √(b²−4ac)) / 2a
System (Cramer's Rule):
x = (c₁b₂ − c₂b₁) / (a₁b₂ − a₂b₁)
y = (a₁c₂ − a₂c₁) / (a₁b₂ − a₂b₁)
Tips
- •If the discriminant is negative, the quadratic has no real solutions — only complex ones.
- •For the system solver, if the determinant is 0 the lines are parallel (no solution) or identical (infinite solutions).
- •Use the Graphing calculator to visualise quadratic equations as parabolas.