Solve the equation cos2x - 5cosx = 2

cos2x= 2cos^2x - 1

2cos^2x - 1 - 5cosx = 2

Let cosx = y

2y^2 - 5y - 3 = 0

(2y + 1)(y + 3) = 0

y = -1/2 or -3

cosx = -1/2 or -3

x = 120 degrees