[latex] \sqrt{3} sin \frac{x}{4} -cos \frac{x}{4}=0[/latex] [latex]3sin ^{2} x-2sinx*cosx-5cos ^{2} x=0[/latex]

[latex] \sqrt{3}sin \frac{x}{4} -cos \frac{x}{4} =0[/latex] [latex]2( \frac{ \sqrt{3} }{2} sin \frac{x}{4} - \frac{1}{2} cos \frac{x}{4})=0 [/latex] [latex]\frac{ \sqrt{3} }{2} sin \frac{x}{4} - \frac{1}{2} cos \frac{x}{4}=0[/latex] [latex] \frac{ \sqrt{3} }{2} =cos \frac{ \pi }{6}, \frac{1}{2} =sin \frac{ \pi }{6} [/latex] [latex]cos \frac{ \pi }{6}sin \frac{x}{4} -sin \frac{ \pi }{6} cos \frac{x}{4} =0[/latex] [latex]sin( \frac{x}{4} - \frac{ \pi }{6} )=0[/latex] [latex] \frac{x}{4} - \frac{ \pi }{6} = \pi k,[/latex] k∈Z [latex] \frac{x}{4} = \frac{ \pi }{6} +\pi k,[/latex] k∈Z [latex]x= \frac{2 \pi }{3}+ \frac{ \pi }{4} k,[/latex] k∈Z