6 син ^2 х - 5 кос х + 5=0

6sin^2 x-5cos x + 5=0

6 (1-cos^2 x) - 5cos x + 5=0

6 - 6cos^2 x - 5cos x + 5=0 / : (-1)

6cos^2 x + 5cos x-11=0

Cos x = t; - 1<=x<=1

6t^2+5t-11=0

D = 25 + 11*4*6=25+264 = 289

T1 = (-5+17) / 12=1

T2 = (-5-12) / 12<-1

Sin x = 1

X = pi/2 + 2pi n