5sin^2 x+4sin x cos x-5cos^2 x=2

5sin^2x+4sinxcosx-5cos^2 x-2sin^2 x-2cos^2 x=0

3sin^2x+4sinxcosx-7cos^2 x=0 / cos^2x

3tg^2x+4tgx-7=0 | tgx=t

3t^2+4t-7=0

D=16+84=100

t1=-4+10/6=-1

t2=-4-10/6=-7/3

tgx=-1 tgx=-7/3

x1=3pi/4 + 2pik x3=arctg (-7/3) + 2pik

x2=7pi/4 + 2pik x4=arctg (-7/3) + pi+2pik