Algebra Calculator

Solve linear equations, quadratic equations, and systems of equations with step-by-step solutions and detailed explanations.

Calculator

Calculator Details

Enter your information to calculate results

Linear Equation: ax + b = 0

Enter the coefficients a and b to solve for x

Equation: 2x + (6) = 0

Results

How It Works

The algebra calculator solves different types of equations using standard algebraic methods:

Linear Equations (ax + b = 0):

x = -b/a

Quadratic Equations (ax² + bx + c = 0):

x = (-b ± √(b² - 4ac)) / (2a)

System of Equations:

Uses Cramer's rule with determinants to find unique solutions

Examples

Linear Example

Equation: 2x + 6 = 0

Solution: x = -3

Quadratic Example

Equation: x² - 5x + 6 = 0

Solutions: x = 2, x = 3

System Example

Equations:

2x + 3y = 7

x - y = 1

Solution: x = 2, y = 1

Compare

Types of Solutions:

  • Linear: One solution, no solution, or infinite solutions
  • Quadratic: Two real solutions, one repeated solution, or complex solutions
  • System: Unique solution, no solution, or infinite solutions

Applications:

  • Physics: Motion equations, force calculations
  • Economics: Supply and demand intersections
  • Engineering: Circuit analysis, structural calculations
  • Optimization: Finding maximum and minimum values