Given the sequence:

u0=3 u1=22

un+2= (12un+1)-(20un)

To find the closed for we use the equation

r^2-12r+20=0

So, why do we use that equation, how does it work? Why are those signs switched, so positive becomes a negative and vice versa?

I know the answer and how to get it, so

un=2^n+2x10^10

I just need some help on how all this works.

Thanks.