Equation Solver

What Is an Equation Solver?

An equation solver is a mathematical tool that calculates the value or values of an unknown variable that make an equation true. The YesTools Equation Solver is designed for polynomial equations in x up to quadratic degree, allowing you to solve common linear and quadratic equations directly in your browser.

Instead of manually rearranging an equation, the solver identifies the coefficients after moving all terms to one side and applies the appropriate mathematical method. It can therefore be useful for students, teachers, homework, revision, algebra practice and anyone who needs to check an equation quickly.

Why Use the Equation Solver?

The calculator is designed to make common algebraic equations quick to solve while still showing the mathematical working behind the result.

How to Use the Equation Solver

Enter a valid equation containing x and an equals sign. The solver supports linear equations and quadratic equations with polynomial terms up to x².

1. Enter the equation — Type an equation such as 2x + 3 = 7 or x² − 5x + 6 = 0 into the input field.
2. Check the format — Use x as the variable and use x² or x^2 for squared terms. Multiplication symbols are optional between a number and x.
3. Select Solve Equation — The calculator moves all terms to one side and determines whether the equation is linear or quadratic.
4. Review the solution — The result, equation type, relevant calculations and step-by-step working are displayed below the input.

How to Solve Equations

Solving an equation means finding the value of the unknown variable that makes both sides equal. The first step is normally to simplify the equation and move all terms to one side so that it can be written in a standard form. For a linear equation, the resulting form is typically ax + b = 0. For a quadratic equation, the standard form is ax² + bx + c = 0.

For example, the equation 2x + 3 = 7 can be solved by subtracting 3 from both sides to obtain 2x = 4, then dividing by 2 to give x = 2. A quadratic equation such as x² − 5x + 6 = 0 has two solutions, x = 2 and x = 3.

Solving Linear Equations

A linear equation contains x only to the first power. After simplifying the equation into ax + b = 0, the solution can be found using x = −b ÷ a, provided that a is not zero. If the x terms cancel completely, the equation may instead have no solution or infinitely many solutions.

Solving Quadratic Equations

A quadratic equation contains an x² term and can be written as ax² + bx + c = 0, where a is not zero. Its solutions can be calculated using the quadratic formula x = (−b ± √(b² − 4ac)) ÷ 2a. The expression b² − 4ac is called the discriminant and determines whether the solutions are real and distinct, real and repeated, or complex.

Equation Solver Results and Limitations

The YesTools Equation Solver supports polynomial equations in one variable, x, up to degree two. This includes linear equations and quadratic equations with constants, positive or negative coefficients and decimal values. Expressions can be entered on either side of the equals sign.

The solver does not evaluate arbitrary higher-degree polynomial equations, trigonometric equations, logarithmic equations, exponential equations or equations containing multiple independent variables. Parentheses and general algebraic functions are also outside the supported input format. For supported equations, the calculator performs the numerical work locally in your browser and displays the relevant solution method.

Frequently Asked Questions