3cos^2x+4sinxcosx+5sin^2x=2

[latex]3cos ^{2} x+4sinxcosx+5sin ^{2} x=2[/latex][latex]3cos ^{2} x+4sinxcosx+5sin ^{2} x-2(sin ^{2} x+cos ^{2} x)=0[/latex][latex]3cos ^{2} x+4sinxcosx+5sin ^{2} x-2sin ^{2} x-2cos ^{2} x=0[/latex][latex]cos ^{2} x+4sinxcosx+3sin ^{2} x=0 [/latex] |:[latex]cos ^{2} x,[/latex]  [latex](cos ^{2} x eq 0)[/latex][latex]1+4 frac{sinx}{cosx} +3 frac{sin^{2}x }{cos ^{2}x } =0[/latex][latex]1+4tgx+3tg ^{2} x=0[/latex][latex]tgx=y[/latex][latex]3y ^{2} +4y+1=0[/latex]D = 4² - 4· 3·1 = 16 - 12 = 4[latex] sqrt{D} =4[/latex][latex]y _{1} = frac{-4+2}{6} = frac{-2}{6} =- frac{1}{3} [/latex][latex]y _{2} = frac{-4-2}{6} = frac{-6}{6} =-1[/latex][latex] left { {{tgx=- frac{1}{3} } atop {tgx=-1}} ight. [/latex][latex]x=-arctg frac{1}{3} + pi n,[/latex] n∈Z[latex]x=- frac{ pi }{4} + pi m,[/latex] m∈Z