2ctg в квадрате x + ctgx -1=0

2ctg²x + ctgx - 1 = 0
ctgx = t
2t² + t - 1 = 0
D = 1² - 4· 2·(-1) = 1 + 8 = 9
$sqrt{D } =3$

$t _{1} = frac{-1+3}{4}= frac{2}{4}= frac{1}{2}$

$t _{2} = frac{-1-3}{4} = frac{-4}{4} =-1$

$left { {{ctgx= frac{1}{2} } atop {ctgx=-1}} right.$

$x=arcctg frac{1}{2} + pi k,$ k∈Z

$x = frac{3 pi }{4} + pi k,$ k∈Z