I am assuming you have some initial condtions?. Something like
or something like that.
You can write it as
Solving, we see
Then,
Now apply your initial condtions to find a and b.
This is a linear constant coefficient homogeneous difference equation. You treat it like a linear constant coefficient homogeneous ODE.
Take trial solution , substitute this into the recurrence to get a quadratic equation for . Solve the quadratic to get two basic solutions, form a general solution as a linear combination of these two solutions.
RonL