A root, zero or solution of equation f(x)=0 are the values of x for which the equation holds true. In the simplest case x can represent one variable (or unknown). But x may also represents a vector of two or more variables.
For elementary linear or quadratic equations, with one variable, finding the roots or zeros (or solution) is straightforward. A typical case of solving for two or more variables is that of solving simultaneous linear equations. Simultaneous linear equations with two variables can be solved on paper fairly easily. Simultaneous linear equations with three or more variables are often solved through writing them in matrix-vector form.
There are numerous methods for finding the roots of an equation. Two of the most popular methods are the Bisection Method and the Newton-Raphson Method and the links also link to spreadsheet demonstrations of the methods.