+128474 3sin^2 x = 8 cos x
3 ( 1 - cos^2 x) = 8 cos x
3 - 3cos^2 x = 8 cos x rearrange as
3cos^2 x + 8cos x - 3 = 0 let cos x = m
3m^2 + 8m - 3 = 0
(3m - 1) ( m + 3) = 0
The second factor has no real solutions for the cosine
So
3m - 1 = 0
3m = 1
m =1/3
So
cos x = 1/3 take the arccos
arccos (1/3) = x ≈ 70.53° + 2pi * n where n is an integer
And
x= 360 - 70.53 ≈ 289.47° + 2 pi * n where n is an integer
