Equations
Enter both sides separated by “=”. One-variable polynomials up to degree two are supported. Quadratic results include the discriminant, roots, and substitution checks.
ALGEBRA CALCULATIONS
Solve equations. Calculate fractions and proportions.
Solve linear and quadratic equations, verify roots, and calculate with exact common fractions. Separate tabs make it easy to switch to the task you need.
Enter a one-variable equation, such as 2x + 3 = 7 or x^2 − 5x + 6 = 0. The calculator rewrites it in standard form, shows the solution steps, and substitutes each root back into the original equation.
The fraction tab can add, subtract, multiply, or divide up to 10 common or mixed fractions in one calculation. It also compares and reduces fractions. Ratios can be reduced or compared, and the proportion solver finds a missing term in a:b = c:d. Decimal values may use a period or comma.
Shows the main inputs and hides explanations.
01 / ALGEBRA CALCULATORCalculations run in your browser
Choose a task
Enter an equation and select Solve equation.
SOLUTION
Enter fractions and choose an operation.
RESULT
Exact value
Simplify a ratio
For example, 1.5 : 2.5 reduces to 3 : 5.
RESULT
Simplest ratio
Compare two ratios
Enter four values to compare.
RESULT
Ratio comparison
Find a missing proportion term
Enter the equality as a : b = c : d. Select which value to solve for.
Try the example or enter your own values.
RESULT
Unknown value
Equations and entered values are processed in your browser. Usage counting sends the operation type and a random browser identifier; the entered values are not sent.
QUICK GUIDE
Three types of algebra problems
Fractions
Enter up to 10 common or mixed fractions. Addition, subtraction, multiplication, and division are applied sequentially from left to right. The exact result is reduced and shown as a mixed number and decimal when applicable.
Ratios
Reduce a ratio, compare it with another pair, or enter a : b = c : d and choose the missing term. Zero denominators and undefined values are checked before calculation.
Frequently asked questions
Which equations can this calculator solve?
It solves one-variable linear and quadratic equations, including polynomials with integer or fractional coefficients. Higher-degree equations and multi-variable systems are not supported here.
How should I enter an equation?
Enter both sides separated by one equals sign, such as 2x + 3 = 7. Use the Latin variable x; multiplication can be explicit (`2*x`) or implicit (`2x`). Parentheses and powers 0, 1, and 2 are supported.
What do the solution steps show?
For a linear equation, the steps isolate the variable and divide by its coefficient. For a quadratic, they show standard form, the discriminant, and the root formula; each root is also substituted back into the equation.
What does “identity” mean?
It is an equation that is true for every x, such as 2x + 2 = 2(x + 1). There are no individual roots because every value of the variable works.
Why does the calculator report no solution?
After moving both sides to one side, the equation reduces to a false numerical statement, such as 0 = 1 for 2x + 2 = 2x + 3. No value of x can satisfy it.
Are complex roots shown?
Yes. A quadratic with a negative discriminant returns complex roots using the imaginary unit i. Their check reports the substitution residual for the original polynomial.
Why are some roots approximate?
When the square root of the discriminant is irrational, the result is shown as a decimal approximation. Rational roots remain in exact fractional form.
Which fraction operations are available?
Add, subtract, multiply, or divide values, compare them, or reduce the first. Enter an integer, 3/4, the mixed number 1 1/2, or a decimal. The result is calculated as an exact rational number.
How is a fraction result displayed?
The main result is an exact reduced fraction or integer. A mixed number and decimal representation are also shown; the decimal does not replace the exact result.
Why can’t I enter a zero denominator?
A fraction with a zero denominator is undefined. Dividing by a fraction equal to zero is also undefined, so the calculator reports the issue instead of returning a value.
How are decimal ratios simplified?
Values are converted to exact decimal fractions and reduced to integers. For example, 1.5 : 2.5 becomes 3 : 5. Negative ratio values are not accepted.
How do I solve a : b = c : d?
Enter the three known terms, select the fourth term to find, and solve. The calculator returns an exact fraction and verifies the equality of cross-products.
What if the proportion has a zero denominator?
If the selected unknown requires division by zero, there is no defined result. Enter valid known values; zero cannot serve as a proportion denominator.
Does the calculator accept a decimal comma?
Yes. Equation coefficients, ratios, and fraction-mode values accept either a decimal point or comma. A decimal is converted to a rational value using the digits entered.
Can I solve a system with several variables here?
No. This tool solves one-variable equations only. Use the matrix calculator for systems in the form A·x=b with multiple equations and unknowns.