can you please explain what this slide is explaining. I want to know how I'd do what it says by hand on paper.

Solving aX(n) + bX(n-1) + cX(n-2) =0 Set up the characteristic equation (quadratic) ar2 + br + c=0 Solve to obtain roots r, and r2 General solution to the recurrence if r, and r, are two distinct real roots: X(n) = ar "+ Br," if r=12 = r are two equal real roots: X(n) = ar" + Burn Particular solution can be found by using initial conditions 36