The root of
an equation is any number which satisfies the equation. It is a
solution of the equation.

For example,

x = 2 is a root of 3x - 1 =
5, as 3 x 2 - 1 = 5, and of x^{2} - 3x + 2 = 0, as 2^{2} - 3
x 2 + 2 = 0.

But x = 1 is also a root of the second equation as 1^{2}
- 3 x 1 + 2 = 0.

Equations are often used to state the equality of two expressions
containing one or more variables. In the reals we can say, for example,
that for any given value of x it is true that

x(x - 1) = x^{2} - x.

(x + 1)^{2} = 2x^{2} + x + 1 is an equation, whose roots are x = 0 and
x = 1. Whether a statement is meant to be an identity or an equation,
carrying information about its variables can usually be determined
from its context.