Algebraic equation

An algebraic equation asserts equality between algebraic expressions built from variables, constants, arithmetic operations, and sometimes roots. Its solutions are values that make the equality true.

Algebraic expression: A combination of variables, constants, and operations that represents a mathematical quantity. Each side of an algebraic equation is an expression whose value is compared.
Equivalent equations: Equations with exactly the same solution set over a specified domain. Valid solving steps replace an equation with one that preserves its solutions.
Linear equation: An equation whose variables occur only to the first power, defining a linear relation. Linear equations model proportional changes and are the simplest nontrivial algebraic equations.
Differential equation: An equation involving an unknown function and one or more of its derivatives. It constrains rates of change, unlike an algebraic equation's relations among quantities.
Variable (mathematics): A symbol that represents a quantity whose value may vary or be unknown. Variables mark the quantities whose values an equation constrains.
Polynomial equation: An equation in which both sides are polynomials in one or more variables. Polynomial equations form a central, structured class of algebraic equations.
Quadratic equation: A polynomial equation of degree two in one variable. Quadratic equations capture curved relationships and have a general solution formula.
Functional equation: An equation in which the unknown is a function and its values at related inputs are connected. Its unknown is a function rather than merely a variable value.
Constant (mathematics): A quantity with a fixed value, unlike a variable whose value can change. Constants supply fixed values within the expressions being equated.
Rational equation: An equation involving rational expressions, which are quotients of polynomials. Clearing denominators can simplify these equations but may introduce forbidden values.

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