3cos^2 x+ 5sinxcosx=-1

3cos²x+5sinxcosx+cos²x+sin²x=0
sin²x+5sinxcosx+4cos²x=0 /cos²x≠0
tg²x+5tgx+4=0
tgx=a
a²+5a+4=0
a1+a2=-5 U a1*a2=4
a1=-4⇒tgx=-4
x=-arctg4+πn
a2=-1⇒tgx=-1⇒x=-π/4+πn