Solve for x Calculator: Equation Solver with Steps

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Formula at a glance

Solve for x Calculator: Linear — ax + b = 0 ⇒ x = −b/a. Example: Linear: 2x + 5 = 17 → Solution: x = 6 — How the Solve for x Calculator works: Linear — ax + b = 0 ⇒ x = −b/a

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📘 About the Solve for x Calculator

Solving an equation means finding the values of the unknown that make both sides equal. Linear equations have one answer, quadratics up to two, cubics up to three, and equations with sin, eˣ or logarithms can have many.

The calculator moves everything to one side and clears fractions. Linear and quadratic equations are solved exactly with the steps shown (including the quadratic formula and complex roots), higher polynomials are factored with the rational root theorem, and other equations are solved numerically. Every solution is substituted back, and values that make a denominator zero are rejected.

🧮 Formula

Linear

ax + b = 0 ⇒ x = −b/a

Quadratic formula

x = (−b ± √(b² − 4ac)) / 2a

Exponential

aˣ = c ⇒ x = log(c)/log(a)

✏️ Worked examples

Linear: 2x + 5 = 17

You enter
Equation	2x + 5 = 17
Variable	x

You get
Solution	x = 6
Equation	2x + 5 = 17
Check x = 6	left = 17, right = 17

x = 6.

Quadratic: x² − 5x + 6 = 0

You enter
Equation	x^2 - 5x + 6 = 0
Variable	x

You get
Solutions	x = 2, x = 3
Equation	x^2 - 5x + 6 = 0
Check x = 2	left = 0, right = 0
Check x = 3	left = 0, right = 0

x = 2, x = 3.

🧭 How to use this calculator

What you enter

EquationNo “=” means “= 0”.
VariableOne letter. Other letters are treated as constants.

What you get

Solution
Equation
Check x = 6

❓ Frequently asked questions

How do I solve for x?

Do the same thing to both sides to get x alone: undo addition with subtraction, multiplication with division. For x² terms use factoring or the quadratic formula.

What if there is no real solution?

Equations like x² + 1 = 0 have no real solution; the calculator gives the complex solutions instead (x = ±i).

What is an extraneous solution?

A value that appears while solving (for example after multiplying by x or squaring) but does not satisfy the original equation. Each answer is checked to catch these.

Can it solve sin x = 0.5?

Yes — it finds the solutions near zero (π/6, 5π/6, …). Trigonometric equations have infinitely many solutions, repeating every 2π.

x= Solve for x Calculator (Equation Solver) with Steps