Wiktionary
n. (context algebra English) A mathematical equation in which one or both sides is an algebraic expression, such as 2x + 7y = 3.
Wikipedia
In mathematics, an algebraic equation or polynomial equation is an equation of the form
P = Q
where P and Q are polynomials with coefficients in some field, often the field of the rational numbers. For most authors, an algebraic equation is univariate, which means that it involves only one variable. On the other hand, a polynomial equation may involve several variables, in which case it is called multivariate and the term polynomial equation is usually preferred to algebraic equation.
For example,
x − 3x + 1 = 0
is an algebraic equation with integer coefficients and
$$y^4+\frac{xy}{2}=\frac{x^3}{3}-xy^2+y^2-\frac{1}{7}$$
is a multivariate polynomial equation over the rationals.
Some but not all polynomial equations with rational coefficients have a solution that is an algebraic expression that can be found using a finite number of operations that involve only those same types of coefficients (that is, can be solved algebraically). This can be done for all such equations of degree one, two, three, or four; but for degree five or more it can only be done for some equations, not for all. A large amount of research has been devoted to compute efficiently accurate approximations of the real or complex solutions of a univariate algebraic equation (see Root-finding algorithm) and of the common solutions of several multivariate polynomial equations (see System of polynomial equations).
Usage examples of "algebraic equation".
In the seventeenth century there were two quite distinct ways of describing the connection between mathematical quantities: you could write an algebraic equation or you could draw a curve.
The Yeunner that blossomed vanished entirely, whisked out of the local space-time continuum the way the mystery of X disappears when an algebraic equation is solved.
It was as though day-to-day twentieth-century living had become an unsolvable algebraic equation.
To do this focusing means to establish a point of reference, as in an algebraic equation in which something is calculated by playing on a third element.
I couldn't wait for the next algebraic equation, a further geometric puzzle or the challenge of solving an arithmetic test in my head while others in the form sucked their pencils as they considered pages of longhand figures.