当 $x$满足 $\left\{\begin{array}{c}2x<4x-4\\ \frac{1}{3}(x-6)>\frac{1}{2}(x-6)\end{array}\right.$时，方程 $x^2-2x-5=0$的根是 $($　　 $)$

A． $1\pm \sqrt{6}$B． $\sqrt{6}-1$C． $1-\sqrt{6}$D． $1+\sqrt{6}$