Introduction
This free Equation Calculator solves math equations step by step. Type in any equation, hit Solve, and get the answer right away. It works with linear equations, quadratic equations, polynomial equations, and more. You can also see a graph of your equation, view each step of the solution, and check your own answer to make sure it is correct.
The calculator supports many types of algebra problems. You can simplify, factor, expand, or find intercepts and vertices. Use Basic Mode for a single equation or switch to Advanced Mode to solve a system of two equations at once. A built-in math keyboard makes it easy to enter special symbols like square roots, exponents, and fractions without a physical keyboard.
How to Use Our Equation Calculator
Enter any math equation into this calculator to get the answer, step-by-step solution, graph, and number line. Here is how each part works.
Solve Mode: Pick Basic Mode if you have one equation with one variable. Pick Advanced Mode if you have two equations with two variables, separated by a comma.
Enter Equation: Type your equation into the input box. Use the equals sign (=) to set both sides. Use ^ for powers, * for multiplication, and sqrt() for square roots. For example, type 2x + 5 = 13 or x^2 - x - 6 = 0. You can also click Math Keyboard to insert symbols.
Solve For: If your equation has more than one variable, use this dropdown to choose which variable you want to solve for.
Solve Over: Choose the number system for your answer. Pick Real Numbers for standard answers, Complex Numbers to include imaginary answers, or Integers Only to show whole number answers.
Quick Actions: Choose what you want the calculator to do. Solve For finds the value of the variable. Simplify reduces the equation. Expand multiplies it out. Factor breaks it into parts. Other options like Intercepts, Vertex, and Critical Points are found under the More button.
Detail Level: After you solve, choose how much work to show. All Steps shows every part of the solution. Key Steps shows only the main parts. Answer Only hides the steps.
Solution Method: For quadratic equations, you can pick how the calculator solves it. Choose from Quadratic Formula, Factoring, or Completing the Square to see different methods.
Press the Solve button or hit Enter to get your results. Use the tabs below the answer to view the Graph, Number Line, Related Equations, and Examples.
What Is an Equation?
An equation is a math statement that says two things are equal. It always has an equals sign (=) in the middle. For example, 2x + 5 = 13 tells us that when you multiply some number by 2 and add 5, you get 13. The goal is to find what number makes this true. That number is the solution.
How to Solve an Equation
To solve an equation, you need to get the variable (usually x) alone on one side. You do this by doing the same thing to both sides. If a number is added, you subtract it from both sides. If a number is multiplied, you divide both sides by it. Each step keeps the equation balanced, like a scale.
Types of Equations
There are several types of equations you may come across:
- Linear equations have no exponents on the variable. They form a straight line on a graph and have one solution. Example: 3x − 7 = 8. You can find the slope and intercepts of these lines.
- Quadratic equations have the variable raised to the second power (x²). They can have zero, one, or two solutions. Example: x² − x − 6 = 0.
- Polynomial equations have higher powers like x³ or x⁴. The degree tells you the most solutions it can have. You can use synthetic division to break these down.
- Radical equations use square roots or other roots. Example: √(x − 1) = 5.
- Absolute value equations use |x|, which gives the distance from zero. Example: |3x + 1| = 4.
- Systems of equations are two or more equations solved at the same time. They share the same variables, and you find values that work in all of them.
Key Terms to Know
- Variable: A letter (like x or y) that stands for an unknown number.
- Coefficient: The number in front of a variable. In 5x, the coefficient is 5.
- Solution (or root): The value that makes the equation true.
- Discriminant: In a quadratic equation ax² + bx + c = 0, the value b² − 4ac. It tells you how many real solutions exist.
Why Equations Matter
Equations are used every day in science, building, money, and technology. When you figure out how much paint covers a wall, how fast a car travels, or how much something costs on sale with a percentage calculation, you are solving equations. Learning to solve them builds strong thinking skills that help in many parts of life.