To solve an equation means to find all the values that make the statement true.
To solve an equation graphically, draw the graph for each side, member, of the equation and see where the curves cross, are equal. The x values of these points, are the solutions to the equation.
There are many possible outcomes when one solves an equation.
Consider the following examples.
The graphic technique of finding where the curves intersect to find the solution works all the time, but, works best when the intersections are easy to find/compute/read.
More examples follow.

The two expressions are equal when x is 1. The solution to the equation is x is 1. The algebraic solution is shown below. 
The two expressions are never equal when real numbers are considered. The solution is a more sophisticated number which involves the square root of a negative numer. The solution is the complex number shown below with the algebraic solution. 