One tool, three kinds of equation
Most school algebra comes down to three shapes: a straight linear equation, a quadratic with a squared term, and a pair of equations solved together. This solver reads which one you have typed and picks the method, rather than making you choose first.
The quadratic formula, and the discriminant
A quadratic is solved with the formula every algebra course drills, but the useful part is the piece under the square root.
| Discriminant | Real roots |
|---|---|
| Positive | Two distinct real roots |
| Zero | One repeated real root |
| Negative | No real roots (they are complex) |
For x² − 5x + 6 the discriminant is 25 − 24 = 1, positive, so there are two real roots: x = 2 and x = 3. Multiply (x − 2)(x − 3) back out to check.
Why the steps matter more than the answer
A solver that only prints a number teaches you nothing. The value here is seeing the working: which method applied, how the discriminant decided the number of roots, how elimination cancelled a variable in a system. Read the steps once and the next one you can do by hand.
Frequently asked questions
What kinds of equations does it solve?
Three kinds. Linear equations in one variable like 2x + 4 = 0; quadratic equations like x² - 5x + 6 = 0; and two-by-two systems of linear equations such as x + y = 5 with x - y = 1. It works out which one you have typed and applies the right method.
How do I type powers and variables?
Use ^ for a power, so x squared is x^2. Multiplication can be implicit — 5x means 5 times x. You can put terms on both sides of the equals sign; the solver moves everything to one side for you before solving.
How is a quadratic solved?
By the quadratic formula, x = (−b ± √(b² − 4ac)) / 2a. The part under the root, b² − 4ac, is the discriminant: positive gives two real roots, zero gives one repeated root, and negative means no real roots. For x² - 5x + 6 the discriminant is 1, giving x = 2 and x = 3.
What does the discriminant tell me?
It tells you how many real solutions a quadratic has before you finish solving it. A positive discriminant means the parabola crosses the x-axis twice, zero means it just touches at one point, and negative means it never crosses, so the roots are complex rather than real.
How does it solve a system of two equations?
By elimination: it scales and subtracts the equations to cancel one variable, solves for the other, then substitutes back. For x + y = 5 and x - y = 1, adding them gives 2x = 6, so x = 3 and y = 2. If the two lines are parallel it reports no unique solution.