# Equation

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A mathematical **equation** is an expression containing at least one variable (=unknown value) and an "equals sign" ( = ) with a mathematical expression on each side of it.<ref>An equation is an equality that is true only for certain values of the variable. Trigonometric identities. Topics in trigonometry.</ref><ref>"A statement of equality between two expressions. Equations are of two types, **identities** and **conditional equations** (or usually simply "equations")". « *Equation* », in *Mathematics Dictionary*, Glenn James et Robert C. James (éd.), Van Nostrand, 1968, 3 ed. 1st ed. 1948, p. 131.</ref><ref>Une équation est une égalité entre deux expressions mathématiques, donc une formule de la forme A = B, où les deux membres A et B de l'équation sont des expressions où figurent une ou plusieurs variables, représentées par des lettres. ÉQUATION, mathématique - Encyclopædia Universalis</ref> The equals sign says that both sides are exactly the same value. An equation can be as simple as x=0, or as hard as 4(3y^99)+76=42÷3x or harder.

There are two kinds of mathematical equations:

- The kind of equation that is either true or false; these are also called identities. For example:

- The kind of equation that lets you calculate the value of one or several variables. The equation is only true if the variable(s) have that value. For example:

The second kind is often used to solve problems in which you have to know the value of some variables. For example,

The second kind of equation is used in algebra. For example, to solve the equation 2x = 8 by finding x you would follow an algebraic rule. Then you can work out that x = 4.

## Types of equations

Equations can be classified by the types of operations and quantities involved. Some types of equations are:

- An algebraic equation is an equation in which both sides are polynomials. These are further classified by degree:
- linear equation for degree one
- quadratic equation for degree two
- cubic equation for degree three
- quartic equation for degree four
- quintic equation for degree five

- A Diophantine equation is an equation where the unknowns are required to be integers
- A differential equation is a functional equation involving derivatives of the unknown functions