I assume you're asked to solve
4 cos²(x) - 7 cos(x) + 3 = 0
Factor the left side:
(4 cos(x) - 3) (cos(x) - 1) = 0
Then either
4 cos(x) - 3 = 0 or cos(x) - 1 = 0
cos(x) = 3/4 or cos(x) = 1
From the first case, we get
x = cos⁻¹(3/4) + 2nπ or x = -cos⁻¹(3/4) + 2nπ
and from the second,
x = nπ
where n is any integer.
