Equation Solver

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

Linear Equation: ax + b = 0

Example: 2x - 6 = 0

Solution: x = 3

Equation Solving Methods

Linear Equations

ax + b = 0
x = -b/a

One solution

Quadratic Formula

x = [-b ± √(b²-4ac)] / 2a

Discriminant: D = b² - 4ac

System of Equations

Substitution
Elimination
Matrix methods

Root Finding

Newton's Method
Bisection Method
Numerical methods

An equation is a statement that asserts the equality of two expressions.

Equation Solver - Solve Linear, Quadratic & System of Equations

Our free equation solver helps students, teachers, and professionals solve mathematical equations instantly with step-by-step solutions. Solve linear equations, quadratic equations, systems of equations, and more with detailed explanations of each solving step.

Perfect for math homework, exam preparation, engineering calculations, and scientific research. Understand the methodology behind solutions rather than just getting answers, making it an invaluable learning tool.

How to Use This Equation Solver

Step 1: Enter Your Equation

  • Input your equation using standard mathematical notation
  • Choose equation type: linear, quadratic, or system
  • Use variables like x, y, z for unknown values

Step 2: Get Step-by-Step Solution

  • View complete solving process with explanations
  • Learn the methods used for each equation type
  • Verify your manual calculations

Why Use Our Equation Solver?

Multiple Equation Types

Solve linear equations, quadratic equations, systems of equations (2x2, 3x3), polynomial equations, and more with specialized algorithms for each type.

Educational Step-by-Step

Learn the solving methodology with detailed explanations for each step, including algebraic manipulations, factoring, and solution verification.

Multiple Solving Methods

Access different solving techniques including substitution, elimination, graphing, quadratic formula, factoring, and completing the square.

Solution Verification

Automatically verify solutions by substituting back into original equations, ensuring accuracy and building confidence in results.

Comprehensive Math Tool

Used by students, teachers, engineers, and researchers worldwide for accurate equation solving and mathematical problem-solving.

Frequently Asked Questions (FAQ)

What types of equations can this solver handle?

Our solver handles linear equations (ax + b = 0), quadratic equations (ax² + bx + c = 0), systems of linear equations (2x2, 3x3), polynomial equations up to 4th degree, and rational equations. Each type uses specialized solving algorithms.

How does the step-by-step solution work?

The step-by-step solution breaks down the solving process into individual algebraic steps with explanations. For example: "Step 1: Subtract 5 from both sides," "Step 2: Divide both sides by 2," showing the reasoning behind each operation.

Can it solve systems of equations with multiple variables?

Yes! Our solver can handle systems of equations with 2 or 3 variables using methods like substitution, elimination, or matrix operations. It provides solutions as ordered pairs or triples (x,y) or (x,y,z).

What if an equation has no solution or infinite solutions?

Our solver correctly identifies no solution (inconsistent equations) and infinite solutions (dependent equations) cases. It explains why these situations occur and provides the appropriate mathematical conclusion.

How accurate are the solutions?

Solutions are mathematically precise using exact fractions and radicals where appropriate. For decimal approximations, we provide results to sufficient precision and show the exact form alongside decimal equivalents.