🧮 Equation Solver

Solve linear equations, quadratic equations, systems of equations, and more with step-by-step solutions

🔧 Multi-Purpose Equation Solver

📏 Linear Equation: ax + b = c
2x + 3 = 7
📐 Quadratic Equation: ax² + bx + c = 0
x² - 5x + 6 = 0
📊 System of 2 Linear Equations
Equation 1: a₁x + b₁y = c₁
Equation 2: a₂x + b₂y = c₂
2x + 3y = 7
x - y = 1
📈 System of 3 Linear Equations
Equation 1: a₁x + b₁y + c₁z = d₁
Equation 2: a₂x + b₂y + c₂z = d₂
Equation 3: a₃x + b₃y + c₃z = d₃
Solution:
🎯 Quick Examples

📚 Understanding Different Types of Equations

📏 Linear Equations

  • Form: ax + b = c
  • Solution: x = (c - b) / a
  • Graph: Straight line
  • Example: 2x + 3 = 7 → x = 2

📐 Quadratic Equations

  • Form: ax² + bx + c = 0
  • Solution: Quadratic formula
  • Graph: Parabola
  • Roots: Can have 0, 1, or 2 real solutions

📊 Systems of Equations

  • 2 Variables: Find intersection point
  • 3 Variables: Find intersection point in 3D
  • Methods: Substitution, elimination, matrix
  • Solutions: Unique, infinite, or no solution

🔧 Solving Steps

  1. Identify equation type
  2. Apply appropriate method
  3. Solve systematically
  4. Check your solution

🌍 Real-World Applications

💼 Business & Economics

Break-even analysis, supply and demand modeling, profit optimization, and cost calculations.

🔬 Science & Engineering

Physics motion problems, chemical reactions, circuit analysis, and engineering design.

🏠 Everyday Problems

Age problems, distance-rate-time problems, mixture problems, and financial calculations.

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