Equation Solver
Solve linear and quadratic equations step by step.
How to Use Equation Solver
- 1Choose Linear or Quadratic mode
- 2Enter the coefficients
- 3Click Solve to see the solution(s) with steps
About Equation Solver
The Equation Solver solves two types of algebraic equations: linear equations of the form ax + b = c, and quadratic equations of the form ax^2 + bx + c = 0. Enter the coefficients and receive the solution(s) with a clear step-by-step explanation of the method used.
For quadratic equations, the solver uses the quadratic formula and handles all three discriminant cases: two distinct real roots (positive discriminant), one repeated real root (zero discriminant), and two complex conjugate roots (negative discriminant). Steps are shown for each case.
All computation runs in your browser with no server calls. This makes the tool ideal for checking homework solutions, understanding algebra steps, and quickly solving equations during study sessions or problem-solving.
Key Features of Equation Solver
- Solve linear equations: ax + b = c for x
- Solve quadratic equations: ax^2 + bx + c = 0 using the quadratic formula
- Handles all discriminant cases: two real roots, one root, or complex roots
- Shows step-by-step solution process for educational purposes
- Accepts integer, decimal, and fractional coefficient inputs
- Handles edge cases like a = 0 for quadratics gracefully
- Instant results with no page reload
- Fully browser-based with no server dependency
Examples
Solve a linear equation
Solve 3x + 5 = 20 for x.
Input
Linear: a=3, b=5, c=20
Output
x = 5 (steps: 3x = 15, x = 5)
Solve a quadratic equation
Find the roots of x^2 - 5x + 6 = 0.
Input
Quadratic: a=1, b=-5, c=6
Output
x = 3 and x = 2 (discriminant = 1, positive)
Common Use Cases
- Checking algebra homework solutions with step-by-step verification
- Solving linear equations in one variable for any subject
- Finding the roots of quadratic equations for math coursework
- Factoring quadratics by finding their roots
- Engineering and physics problems involving quadratic relationships
- Learning the quadratic formula by seeing it applied with real numbers
Troubleshooting
Setting a = 0 in quadratic mode
Solution
If a = 0, the equation is linear (bx + c = 0), not quadratic. Switch to linear mode or ensure a is non-zero for quadratic solving.
Expecting real roots when the discriminant is negative
Solution
A negative discriminant means the quadratic has no real roots — only complex conjugate roots. The calculator will show the complex form (e.g., 2 + 3i and 2 - 3i).
Entering the equation in the wrong format
Solution
The solver requires you to enter coefficients separately (a, b, c), not the full equation as a string. Rearrange your equation to standard form first.
Frequently Asked Questions
What types of equations can the solver handle?
Linear equations (ax + b = c) and quadratic equations (ax^2 + bx + c = 0). For cubic or higher-degree equations, the solver is not applicable.
What is the quadratic formula?
x = (-b +/- sqrt(b^2 - 4ac)) / (2a). The discriminant b^2 - 4ac determines whether there are two real roots (positive), one root (zero), or two complex roots (negative).
What does a negative discriminant mean?
A negative discriminant means the square root is imaginary, so the quadratic has no real solutions. The roots are complex numbers of the form a + bi and a - bi.
Can I solve equations with decimal coefficients?
Yes. Enter decimal values for a, b, and c (e.g., 0.5, 2.3, -1.7). The calculator handles all real number coefficients.
How do I convert my equation to the standard form?
For linear: rearrange to ax + b = c. For quadratic: rearrange to ax^2 + bx + c = 0 by moving all terms to one side.
What if a = 0 in the quadratic form?
If a = 0, the equation reduces to a linear equation bx + c = 0. The solver handles this as a special case, but it is cleaner to use linear mode directly.
Does the solver show intermediate steps?
Yes. Each step of the solution process is displayed, from identifying the discriminant value to substituting into the quadratic formula and simplifying.
Is my data private?
Yes. All calculations run entirely in your browser. No equation data is transmitted to any server.