Algebra Calculator

Solve linear equations, quadratic equations, and work with ratios and proportions.

Why & What

Algebra is the branch of mathematics that uses symbols (usually letters) to represent unknown values. It provides the foundation for solving real-world problems by expressing relationships as equations.

Linear equations (ax + b = c) have one solution and represent straight lines. Quadratic equations (ax² + bx + c = 0) can have zero, one, or two solutions and represent parabolas. Ratios and proportions help us understand relative quantities and scaling.

Formulas

Linear: ax + b = c → x = (c - b) / a
Solving for x in a linear equation
Quadratic: x = (-b ± √(b² - 4ac)) / 2a
Quadratic formula for ax² + bx + c = 0
Discriminant: Δ = b² - 4ac
Δ > 0: two real roots, Δ = 0: one root, Δ < 0: complex roots
Proportion: a/b = c/d → ad = bc
Cross-multiplication for solving proportions

Linear Equation Solver (ax + b = c)

Educational Purpose Only: This calculator is provided for learning and educational purposes. For critical applications or professional use, please verify results with appropriate professional tools and expertise.

Quadratic Equation Solver (ax² + bx + c = 0)

Proportion Solver (a/b = c/x)

Examples

Linear Equation Example

Solve: 3x + 7 = 22

Using x = (c - b) / a: x = (22 - 7) / 3 = 15 / 3 = 5

Quadratic Equation Example

Solve: x² - 5x + 6 = 0

Discriminant: (-5)² - 4(1)(6) = 25 - 24 = 1 > 0 → two real roots

x = (5 ± 1) / 2 → x₁ = 3, x₂ = 2

Proportion Example

If 3 apples cost $4, how much do 9 apples cost?

3/4 = 9/x → x = (4 × 9) / 3 = $12

Limitations & Disclaimer

Important Limitations
  • This calculator is for educational purposes only.
  • Linear equations require a ≠ 0 (otherwise, no unique solution exists).
  • Quadratic equations may have complex roots when discriminant < 0.
  • Results are subject to floating-point precision limitations.
  • Always verify results for critical applications.