Math

Solve for X Calculator

Find the Value of X in Any Equation

Need to solve for x? Enter the coefficients of your equation and get the answer instantly. This calculator handles both quadratic equations (ax² + bx + c = 0) and linear equations (when a = 0). Whether you are working on algebra homework or solving real-world problems, find x quickly and accurately.

Quick Tips

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Try an Example

Pick a scenario to see how the calculator works, then adjust the values

Standard Form

Classic quadratic x² − 5x + 6 = 0 with two integer roots (x = 2 and x = 3)

Key values: a = 1 · b = −5 · c = 6

Physics Problem

Projectile height equation −4.9t² + 20t + 1.5 = 0 (when does the ball hit the ground?)

Key values: a = −4.9 · b = 20 · c = 1.5

Complex Roots

Equation x² + 2x + 5 = 0 with no real solutions (discriminant < 0)

Key values: a = 1 · b = 2 · c = 5

Documentation

This calculator is also known as Solve for X Calculator.

Read the complete guide

What Does It Mean to Solve for X?

Solving for x means finding the value (or values) of x that make the equation true. For a linear equation like 3x + 9 = 0, there is one answer (x = -3). For a quadratic equation like x² - 5x + 6 = 0, there can be two answers (x = 2 and x = 3).

Examples

Solving a Simple Quadratic

Two numbers add to 15 and multiply to 54. This gives x² - 15x + 54 = 0.

The discriminant is 9, so x = (15 ± 3) / 2, giving x = 9 and x = 6. The two numbers are 6 and 9.

Key takeaway: Many number puzzles and word problems reduce to quadratic equations that can be solved with this calculator.

Getting Started with Solving Equations

Build your equation-solving skills:

Start by writing your equation in the form ax² + bx + c = 0
Identify a (the x² coefficient), b (the x coefficient), and c (the constant)
If there is no x² term, set a = 0 and the calculator solves the linear equation
Always check your answer by plugging it back into the original equation

Frequently Asked Questions about Solve for X Calculator

What if a = 0?

If a = 0, the equation becomes linear (bx + c = 0), and the calculator solves it as x = -c/b. This is a simpler one-step solution.

Can I solve for x when there are complex roots?

Yes! When the discriminant is negative, the solutions are complex numbers in the form a + bi. The calculator displays both the real and imaginary parts.

How do I know if my equation is quadratic or linear?

A quadratic equation has a non-zero x² term (a ≠ 0). If a = 0, the equation is linear (bx + c = 0) and has exactly one solution: x = -c/b. This calculator handles both cases automatically.