2 - 3 sin(3pi/2 + x) + cos^2(x/2) = sin^2(x/2)

2-3sin(3π/2+x)+cos²(x/2)-sin²(x/2)=0
2+3sinx+cos²(x/2)-sin²(x/2)=0
2sin²(x/2)+2cos²(x/2)+6sin(x/2)cos(x/2)+cos²(x/2)-sin²(x/2)=0
sin²(x/2)+6sin(x/2)cos(x/2)+3cos²(x/2)=0/cos²(x/2)
tg²(x/2)+6tg(x/2)+3=0
tg(x/2)=a
a2+6a+3=0
D=36-12=24
a1=(-6-2√6)/2=-3-√6⇒tg(x/2)=-3-√6⇒x/2=-arctg(3+√6) +πn⇒x=-1arctg(3+√6) +2πn
a2=-3+√6⇒tg(x/2)=√6-3⇒x/2=arctg(√6-3)+πn⇒x=2arctg(√6-3)+2πn