Do you not know how to solve a quadratic equation?
But more to the point, that equation can be written Now, an equation like that will have only one root provided it is a double root. That is, if it is of the form .
My work disagrees slightly with HallsofIvy, however:
For this quadratic to have a single root, the discriminant must be 0:
Substituting this back into the original equations gives the system
A single solution, as desired.