Single Variable Equation Calculator

Instantly solve linear, quadratic, and cubic equations. Get detailed solutions with exact and decimal results.

Single Variable Equation Calculator

Quadratic Equation

Form: ax² + bx + c = 0

x^2

x

+=0

Quick Examples

Linear

$2x + 4 = 0$

$x = -2$

Quadratic

$x^2 - 5x + 6 = 0$

$x = 2, 3$

Cubic

$x^3 - 6x^2 + 11x - 6 = 0$

$x = 1, 2, 3$

Understanding Single Variable Equations

A single variable equation is a mathematical statement that equates two expressions containing a single unknown variable, typically denoted as 'x'. This tool specializes in solving polynomial equations of degrees one, two, and three: Linear, Quadratic, and Cubic. It provides comprehensive solutions, offering both exact values (involving fractions and radicals) and decimal approximations for practical use.

Equation Types

Linear Equation

ax + b = 0

A first-degree equation representing a straight line. It always has exactly one unique solution.

2x + 4 = 0 → x = -2

Quadratic Equation

ax² + bx + c = 0

A second-degree polynomial equation forming a parabola. It can yield two distinct real solutions, one repeated real solution, or no real solutions (complex roots).

x² - 5x + 6 = 0 → x = 2 or x = 3

Cubic Equation

ax³ + bx² + cx + d = 0

A third-degree polynomial equation. It always possesses at least one real solution and can have up to three distinct real roots.

x³ - 6x² + 11x - 6 = 0 → x = 1, 2, or 3

Tips for Using the Calculator

•Input Flexibility: You can enter coefficients as integers, decimals (e.g., 0.5), or fractions (e.g., 1/2).
•Leading Coefficient: For the equation to maintain its degree (e.g., to remain quadratic), the first coefficient 'a' must be non-zero.
•Result Formats: Toggle between 'Show Exact' for precise mathematical forms (surds/fractions) and 'Show Decimal' for numerical approximations.
•Real Solutions Only: This calculator focuses on finding real number solutions. Complex or imaginary roots are not currently displayed.
•Cubic Properties: Remember that every cubic equation is guaranteed to have at least one real root.

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