Equation Solver
This equation solver finds x for you: type the equation with x, brackets and fractions allowed, and get the solution with the steps and a check. Example: 3(x − 2) + 4 = 2x + 5 gives x = 7. It works as a linear equation calculator and also solves quadratic and higher-degree equations.
Source: Wolfram MathWorld – Linear equation. Updated: .
How it is calculated
Solving an equation means finding the value of the unknown x that makes both sides equal. The solver handles linear, quadratic and higher-degree equations in one unknown – exact as a fraction where possible, otherwise as a decimal.
How the solver works
- Expand and simplify: brackets are multiplied out and like terms combined.
- Everything on one side: L = R becomes L − R = 0 (standard form).
- Solve: for degree 1, x = −b / a. For degree 2, the quadratic formula with the discriminant D = b² − 4ac helps. For higher degrees, rational solutions are searched for and split off.
- Check: the solution is substituted into both sides.
Examples
- Linear: 3(x − 2) + 4 = 2x + 5 → 3x − 2 = 2x + 5 → x = 7. Check: left 19, right 19.
- Quadratic: x² − 5x + 6 = 0 → x = 2 or x = 3.
- Fraction: x/2 + x/3 = 5 → (5/6)x = 5 → x = 6.
- No solution: x + 1 = x + 2 gives −1 = 0, a contradiction.
Notation
Write powers with ^ or superscripts (x^2 or x²), fractions with /; multiplication signs are optional (2x and 2*x are the same). Decimals may use a point or a comma. Equations with more than one unknown, or with roots or x in a denominator, are not solved here.
Frequently asked questions
How do you solve a linear equation?
Move all terms with x to one side and all numbers to the other, then divide by the factor in front of x. 2x + 3 = 11 becomes 2x = 8 and x = 4.
How do you solve a quadratic equation?
With the formula x = (−b ± √D) / 2a, D = b² − 4ac. If D is positive there are two solutions, if D = 0 one, and if D is negative no real ones (only complex).
What does “no solution” or “every number is a solution” mean?
If x disappears completely while rearranging, what remains is either a false statement (for example −1 = 0, no solution) or an always true one (0 = 0, every number is a solution).
What is the check for?
It substitutes the solution into both sides. If the results are equal, the solution is right; this is how you spot calculation mistakes.
Can the solver handle higher-degree equations?
Yes, up to degree 12: it finds rational solutions exactly, splits them off and gives approximate values, including complex ones, for the rest.
Sources and legal basis
- Wolfram MathWorld – Linear equation
- Wolfram MathWorld – Quadratic equation
- Wolfram MathWorld – Rational root theorem
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