What is the difference between a function and an equation?

A function describes a relation between several variables. For example the function f(x)=x2 describes a mapping from the variable x to a value that is the square of x. That is, for every real number we put as x, we will get a value for f(x). A function is defined for some domain and gets values from some range.

An equation takes two terms and says they are equal. Usually both terms are functions of the same variable(s). For example, to build the equation x2 = x+2,

we will use f(x) = x2, g(x) = x+2 and say that f(x)=g(x).

Solving an equation means finding the set of values of the equation's variables which satisfy the equation. This set of values has to be part of the domains of the functions in both terms of the equation.