The intersection points of the graphs of =3x2−14x and y=x can be found by solving the system consisting of these two equations. To solve the system, substitute x for y in the first equation. This gives x=3x2−14x. Subtracting x from both sides of the equation gives 0=3x2−15x. Factoring 3x out of each term on the left-hand side of the equation gives 0 =3x(x − 5). Therefore, the possible values for x are 0 and 5. Since y=x, the two intersection points are (0,0) and (5,5). Therefore, a=5.