[tex]\displaystyle 2sin^2x+1.5*2sinx*cosx-3cos^2x-(cos^2x+sin^2x)=0\\\\sin^2x+3sinx*cosx-4cos^2x=0\bigg| :cos^2x\neq 0\\\\tg^2x+3tgx-4=0\\\\D=9+16=25\\\\tgx=\frac{-3 \pm 5}{2}\\\\tgx=1; x=\frac{\pi }{6}+\pi n; n\in Z\\\\tgx=-4; x=-arctg4+\pi n; n\in Z[/tex]
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[tex]\displaystyle 2sin^2x+1.5*2sinx*cosx-3cos^2x-(cos^2x+sin^2x)=0\\\\sin^2x+3sinx*cosx-4cos^2x=0\bigg| :cos^2x\neq 0\\\\tg^2x+3tgx-4=0\\\\D=9+16=25\\\\tgx=\frac{-3 \pm 5}{2}\\\\tgx=1; x=\frac{\pi }{6}+\pi n; n\in Z\\\\tgx=-4; x=-arctg4+\pi n; n\in Z[/tex]