Equation Solver Calculator

Author: Henrick Yau
- 7 December 2025
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Calculators

Solve different types of equations including linear, quadratic, cubic, and systems of linear equations. This calculator provides step-by-step solutions, graphical representations, and explains the methods used to find solutions.

Equation Solver

Solve a linear equation in the form ax + b = 0

2x - 10 = 0

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About Equation Solving

Equation solving is a fundamental concept in mathematics that involves finding values of variables that satisfy a given equation. Different types of equations require different solving techniques.

Types of Equations
  • Linear Equations: Equations of the form ax + b = 0, where a and b are constants and a ≠ 0.
  • Quadratic Equations: Equations of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
  • Cubic Equations: Equations of the form ax³ + bx² + cx + d = 0, where a, b, c, and d are constants and a ≠ 0.
  • Systems of Linear Equations: Multiple linear equations that share the same variables, solved simultaneously.
Common Solution Methods
  • Linear Equations: Isolate the variable by performing inverse operations.
  • Quadratic Equations: Factoring, completing the square, or using the quadratic formula.
  • Cubic Equations: Rational root theorem, polynomial division, or Cardano's formula.
  • Systems of Linear Equations: Substitution, elimination, or matrix methods (Cramer's rule, Gaussian elimination).
Applications

Equation solving has many practical applications including:

  • Physics (motion, force, energy)
  • Engineering (stress, strain, circuit analysis)
  • Economics (supply and demand, cost optimisation)
  • Computer science (algorithms, graphics)
  • Finance (investment planning, interest calculations)