# 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:

- [math]2 \cdot (x+4)=2x+8 \rightarrow true[/math]

- 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:

- [math]2 \cdot x=8 \rightarrow x=4[/math]

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

- [math] \text{if}\, 2x = 8, \, x = \frac{8}{2} = 4. [/math]

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