2ctg^2x+ctgx-6=0 решите пж

[latex]2 ctg ^{2} x+ctg x-6=0 \\ ctg x=t \\ 2t ^{2} +t-6=0 \\ D=1+48=49 \\ t _{1} = \frac{-1-7}{4} =-2 \\ t _{2} = \frac{-1+7}{4} = \frac{6}{4} = \frac{3}{2} \\ 1. ctg x=-2 \\ x=arcctg(-2)+ \pi k \\ x= \pi -arcctg 2+ \pi k \\ 2.ctg x= \frac{3}{2} \\ x=arcctg \frac{3}{2} + \pi k [/latex]