3 sin^2 x-3sinx cosx -4 cos^2 x= -2

$3sin^2x-3sinxcosx-4cos^2x=-2 \\ 3sin^2x-3sinxcosx-4cos^2x+2(cos^2x+sin^2x)=0 \\ 3sin^2x-3sinxcosx-4cos^2x+2cos^2x+2sin^2x=0 \\ 5sin^2x-3sinxcosx-2cos^2x=0|:cos^2x \neq 0 \\ 5tg^2x-3tgx-2=0$

Замена: $tgx=a$

$5a^2-3a-2=0 \\ D=9+4*5*2=49 \\ a_1= \frac{3+7}{10}=1 \\ a_1= \frac{3-7}{10}= \frac{-4}{10}=-0.4$

$tgx=1$ или $tgx=-0.4$
$x= \frac{ \pi }{4}+ \pi k,$ k∈Z или $x=arctg(-0.4)+ \pi n,$ n∈Z
$x=-arctg0.4+ \pi n,$ n∈Z