6*cos^2 (x) + 7*sin (x) - 8 = 0

6 (1-sin^2) + 7sinx-8=0

6-6sin^2x+7sinx-8=0

6sin^2x-7sinx+2=0

sinx=y

6y^2-7y+2=0

D=49-48=1

x1=2/3

x2=1/2

1) sinx=2/3

x = (-1) ^n*arcsin2/3+Пn

2) sinx=1/2

x = (-1) ^n*arcsin1/2+Пn

x = (-1) ^n*П/6+Пn