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An equation is a mathematical statement that may (or may not) be true, defined for some variables. Solving an equation is finding those values of the variables for which the equation or statement is true.
to find the unknown variables
The variables of this equation are your letters: a, b, and c. Variables merely stand in an equation to represent values that we don't know. "Solving" an equation is the process by which we uncover those values. In this particular case, since there are three variables, we cannot discover their values unless we have two other equivalent equations (a system of equations).
You don't use unknown variables to solve an equation. The purpose of solving an equation is to find the value of the variable so that it's no longer unknown.
The roots of an equation in two variables is calculated by setting the dependent variable, y, equal to 0 and then solving the resulting equation for the independent variable, x. The procedure for solving the equation in x will depend on the nature of the equation.