![image](https://tex.z-dn.net/?f=tgx%2B6ctgx-5%3D0+%5C%5C+%5Cfrac%7B1%7D%7Bctgx%7D+%2B6ctgx-5%3D0+%7C+%2Actgx+%5C%5C+1%2B6+ctg%5E%7B2%7D+x-5ctgx%3D0+%5C%5C+ctgx%3Dt%2C+t%3E0+%5C%5C+6+t%5E%7B2%7D+-5t%2B1%3D0+%5C%5C+D%3D5%2A5-4%2A6%3D25-24%3D1+%5C%5C+t_%7B1%7D+%3D+%5Cfrac%7B5%2B1%7D%7B12%7D+%3D+%5Cfrac%7B6%7D%7B12%7D+%3D+%5Cfrac%7B1%7D%7B2%7D+%5C%5C+t_%7B2%7D+%3D+%5Cfrac%7B5-1%7D%7B12%7D+%3D+%5Cfrac%7B4%7D%7B12%7D+%3D+%5Cfrac%7B1%7D%7B3%7D+%5C%5C+ctgx%3D+%5Cfrac%7B1%7D%7B2%7D+%5C%5C+x_%7B1%7D+%3Darcctg+%5Cfrac%7B1%7D%7B2%7D%2B%5Cpi+n%2C+n+E+z+%5C%5C+ctgx%3D+%5Cfrac%7B1%7D%7B3%7D+%5C%5C+x_%7B2%7D+%3Darcctg+%5Cfrac%7B1%7D%7B3%7D%2B%5Cpi+n%2C+n+E+z)
0 \\ 6 t^{2} -5t+1=0 \\ D=5*5-4*6=25-24=1 \\ t_{1} = \frac{5+1}{12} = \frac{6}{12} = \frac{1}{2} \\ t_{2} = \frac{5-1}{12} = \frac{4}{12} = \frac{1}{3} \\ ctgx= \frac{1}{2} \\ x_{1} =arcctg \frac{1}{2}+\pi n, n E z \\ ctgx= \frac{1}{3} \\ x_{2} =arcctg \frac{1}{3}+\pi n, n E z" alt="tgx+6ctgx-5=0 \\ \frac{1}{ctgx} +6ctgx-5=0 | *ctgx \\ 1+6 ctg^{2} x-5ctgx=0 \\ ctgx=t, t>0 \\ 6 t^{2} -5t+1=0 \\ D=5*5-4*6=25-24=1 \\ t_{1} = \frac{5+1}{12} = \frac{6}{12} = \frac{1}{2} \\ t_{2} = \frac{5-1}{12} = \frac{4}{12} = \frac{1}{3} \\ ctgx= \frac{1}{2} \\ x_{1} =arcctg \frac{1}{2}+\pi n, n E z \\ ctgx= \frac{1}{3} \\ x_{2} =arcctg \frac{1}{3}+\pi n, n E z" align="absmiddle" class="latex-formula">