Equation Solver
Solve linear equations, quadratics, two-equation systems and inequalities - with every step written out the way your teacher expects.
Solve it
Solves ax + b = 0. Example: 2x - 8 = 0 gives x = 4.
Solves \(ax^2 + bx + c = 0\) with the quadratic formula, showing every step.
Solves a1*x + b1*y = c1 and a2*x + b2*y = c2 by elimination.
Solves ax + b ? 0 and reminds you when the sign flips.
Step by step
- 1x² + -5x + 6 = 0
- Discriminant Δ = b² − 4ac = -5² − 4·1·6 = 1
- Δ > 0, so two real roots: x = (−b ± √Δ) / 2a
- x₁ = (5 + √1) / 2 = 3
- x₂ = (5 − √1) / 2 = 2
How the Quadratic Formula Works
Every quadratic \(ax^2 + bx + c = 0\) is solved by one formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). The part under the root, \(b^2 - 4ac\), is called the discriminant. It tells you what kind of answers to expect: positive means two different real answers, zero means one repeated answer, negative means the answers involve imaginary numbers.
The solver above shows each stage. For \(x^2 - 5x + 6 = 0\), the discriminant is 25 - 24 = 1, so \(x = \frac{5 \pm 1}{2}\), giving \(x = 3\) or \(x = 2\). Check either answer by putting it back into the original equation.
Solving Two Equations Together
Two equations with two unknowns describe two lines. The solution is the point where they cross. Elimination is the tidiest method: multiply the equations so one variable has matching coefficients, subtract to make it vanish, solve for the survivor, then substitute back. The calculator narrates each move so you can copy the working.
Inequalities and the Sign Flip
Inequalities solve almost like equations, with one famous trap: dividing or multiplying by a negative number flips the sign. So -2x < 6 becomes x > -3. Forgetting the flip is the most common inequality mistake, and the solver flags it whenever it happens.
My saved numbers reuse them in any calculator
Save a number once — like your rent or hourly rate — then just type its name instead of the number, in any calculator here. You can also type formulas like 5000 * 1.1 right into any box.
Saved only in this browser — nothing is sent to us.
Frequently Asked Questions
How do you solve a quadratic equation?
Use the quadratic formula: x = (-b +/- sqrt(b^2 - 4ac)) / 2a. First compute the discriminant b^2 - 4ac: if it is positive you get two real answers, if zero one repeated answer, if negative the answers are complex.
What is the discriminant?
The discriminant is b^2 - 4ac, the part under the square root in the quadratic formula. It predicts the answers before you finish: positive means two real roots, zero means one, negative means complex roots.
How do you solve two equations with two unknowns?
Use elimination: multiply the equations so one variable matches, subtract to remove it, solve for the other, then substitute back. Geometrically, the answer is where the two lines cross.
When does an inequality sign flip?
When you multiply or divide both sides by a negative number. For example, -2x < 6 becomes x > -3. Forgetting the flip is the most common inequality mistake.
What does "no solution" mean?
It means no value of x can satisfy the equation - for example 0x + 5 = 0 simplifies to 5 = 0, which is false. For a 2x2 system it means the lines are parallel and never meet.