6 sin ^2x - cos x - 4 = 0

[latex]6 \sin ^2x - \cos x - 4 = 0;\, 6 -6 \cos ^2x - \cos x - 4 = 0;\,[/latex] [latex]6 \cos ^2x + \cos x - 2 = 0;\, \cos x=t;\, 6t^2+t-2=0;\,D=49=7^2;[/latex] [latex]t_1= \frac{-1+7}{12}= \frac{1}{2};\, t_2= \frac{-1-7}{12}= -\frac{2}{3};[/latex] [latex]\, x_1=\pm \frac{ \pi}{3}+2\pi k,\,k\in\mathbb{Z};\, x_2=\pm \arccos( -\frac{2}{3})+2\pi n,\,n\in\mathbb{Z} [/latex]