5sin² x-3sin x cos-2cos² x=0

5sin^2-3sin x cos x - 2cos^2=0

Делим на cos x:

5tg^2-3tgx-2=0

Tg x = t

5t^2-3t-2=0

t=1
t= -2/5

Tg x = 1
x= p/4+pk

Tg= -2/5
x= -arctg 2/5 + pn