4 sin^2 (x/2) + 8 cos (x/2) -7 = 0

4-4сos²(x/2)+8cos(x/2)-7=0
cos(x/2)=a
4a²-8a+3=0
D=64-48=16
a1=(8-4)/8=1/2⇒cos(x/2)=1/2⇒x/2=+-π/3+2πn⇒x=+-2π/3+4πn,n∈z
a2=(8+4)/8=1,5⇒cos(x/2)=1,5>1 нет решения