Algebra Calculator

Solve linear and quadratic equations, clear fractions, expand brackets, and work through systems of equations. Every answer comes with the steps and an exact fraction or surd where one exists.

Use ^ for powers, / for fractions, and put each equation of a system on its own line.

Insert a symbol
Try one of these

Your answer will appear here

Type an equation above or tap an example to see the worked solution.

Get the answer and the reasoning behind it

An answer on its own does not help much when you are stuck on a homework problem or revising for an exam. This calculator shows the same steps a teacher would write on the board, from clearing fractions to reading off the discriminant, so you can find the exact line where your own attempt went wrong.

Linear · Quadratic · Systems

Why use this algebra calculator?

Exact answers, not rounded ones

Coefficients are stored as fractions, so 1/3 stays 1/3 and irrational roots keep their square root. A rounded decimal appears underneath when you need one.

Handles fractions and denominators

Equations such as x/2 + x/3 = 10 and 1/x + 2 = 5 work as typed. The calculator clears the denominators and warns you about the values that would divide by zero.

Systems of equations

Enter two or three equations on separate lines and the elimination method runs automatically, including the cases with no solution or infinitely many.

Nothing leaves your browser

The parser and the solver are plain JavaScript running on your device. No account, no upload, no limit on how many problems you work through.

How this Algebra Calculator works

Type an equation and this calculator reads it the way a person does: left side, equals sign, right side. It splits the input into numbers, letters, and operators, then rebuilds it as a polynomial that stores every coefficient as an exact fraction. That is why one third stays 1/3 and never drifts into 0.3333.

What happens next depends on what you typed. If a variable sits in a denominator, the calculator multiplies both sides by that denominator first and records which values you now have to exclude. It then moves every term to the left so the equation reads "something = 0" and collects like terms.

From there the degree decides the method. A first-degree equation gets divided by the coefficient of the variable. A second-degree equation goes through the quadratic formula, where the discriminant tells you whether you get two clean numbers, one repeated number, a square root that will not cancel, or a complex pair. Cubic and quartic equations rarely factor by hand, so the calculator traces the curve, finds each point where it crosses zero, and narrows every crossing to about six decimal places.

Put two or three equations on separate lines and it switches to elimination instead, clearing one unknown at a time until each variable stands alone.

Every step appears under the answer, so you can compare your own work line by line and spot exactly where a mistake crept in. Nothing is uploaded — the arithmetic runs entirely in your browser.

How to use this Algebra Calculator

1

Type the equation

Write it the way it appears on paper, for example 3x + 5 = 20. Use ^ for powers and / for fractions.

2

Press Solve

The calculator picks the right method on its own: division for linear equations, the quadratic formula for squares, elimination for systems.

3

Read the working

Compare each step against your own, then copy the answer or open the graph to see where the curve meets the x-axis.

Example Usage

Solving a system of two linear equations with two unknowns:

Input
2x + 3y = 12 x - y = 1
Output
x = 3, y = 2 Step 1 Rewrite both equations with all terms on the left Step 2 Eliminate y, then x Step 3 Substitute back: x = 3, y = 2

Frequently Asked Questions

What kinds of equations does this algebra calculator solve?
It handles linear equations such as 3x + 5 = 20, quadratic equations such as x^2 - 5x + 6 = 0, equations with fractions on either side, equations where the variable sits in a denominator, and linear systems with two or three unknowns. It also expands brackets and combines like terms when you leave the equals sign out.
How do I type powers, fractions, and multiplication?
Use ^ for a power, so x squared is x^2. Use / for a fraction, so two thirds is 2/3. Multiplication works either way: 2x and 2*x both mean the same thing, and (x+1)(x-2) multiplies the two brackets.
Can it solve two equations with two unknowns?
Yes. Put each equation on its own line, or separate them with a semicolon. The calculator uses elimination and shows the reduced form. You need at least one equation per unknown, so two unknowns need two equations.
Why does the answer show a fraction instead of a decimal?
Fractions are exact and decimals often are not. When you solve 3x = 1, the honest answer is 1/3, not 0.3333. The calculator prints the fraction first and adds a rounded decimal underneath when the fraction does not terminate.
What is the discriminant and why does it appear?
The discriminant is b squared minus 4ac. If it is positive, the equation has two different real answers. If it is zero, both answers are the same number. If it is negative, the answers are complex and the parabola never touches the x-axis.
Why did the calculator say there is no solution when my equation clearly has an x in it?
Sometimes the x terms cancel each other out. In 4x = 4x + 1, subtracting 4x from both sides leaves 0 = 1, which is false, so no value of x can ever work. The opposite also happens: 4x = 4x reduces to 0 = 0, which is true for every value.
What does the note about values that are not allowed mean?
When a variable appears in a denominator, some values would divide by zero. In 1/x + 2 = 5, the value x = 0 is impossible, so it gets excluded. If the algebra produces a root that breaks a denominator, the calculator drops it and tells you.
Can I use this to check my homework?
That is the main reason it shows the working. Solve the problem yourself first, then compare each line against the steps here. If the answers differ, the step where they split apart is usually the line with the mistake.
Does it solve inequalities such as x > 5?
Not yet. The calculator reads an equals sign, so replace the inequality with an equals sign to find the boundary value, then decide which side of that boundary satisfies the original statement.
Is anything I type sent to a server?
No. The parser and the solver both run in your browser, so your equations never leave your device. Nothing is stored and no sign-up is needed.
Why are cubic answers shown as decimals?
Most cubic and quartic equations have no tidy fraction or square-root form. The calculator traces the curve, finds every point where it crosses zero, and narrows each crossing down to roughly six decimal places.

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