$\left(1\right)x^{2}-9=0$，
$x^{2}=9$，
$\therefore x=\pm 3$，
$\therefore x_{1}=3$，$x_{2}=-3$；
$(2)$解法一：$2x^{2}-4x-1=0$，
$\because a=2$，$b=-4$，$c=-1$，
$\therefore \Delta =b^{2}-4ac=\left(-4\right)^{2}-4\times 2\times \left(-1\right)=24 \gt 0$，
$\therefore x=\frac{4±\sqrt{24}}{2×2}=\frac{2±\sqrt{6}}{2}=1±\frac{\sqrt{6}}{2}$，
$\therefore {x}_{1}=1+\frac{\sqrt{6}}{2}，{x}_{2}=1-\frac{\sqrt{6}}{2}$.
解法二：$2x^{2}-4x-1=0$，
$2x^{2}-4x=1$，
$x^{2}-2x=\frac{1}{2}$，
$x^{2}-2x+1=\frac{3}{2}$，
$\therefore \left(x-1\right)^{2}=\frac{3}{2}$，
$\therefore x-1=\pm \frac{\sqrt{6}}{2}$，
$\therefore {x}_{1}=1+\frac{\sqrt{6}}{2}，{x}_{2}=1-\frac{\sqrt{6}}{2}$.

$\left(1\right)x^{2}-9=0$，
$x^{2}=9$，
$\therefore x=\pm 3$，
$\therefore x_{1}=3$，$x_{2}=-3$；
$(2)$解法一：$2x^{2}-4x-1=0$，
$\because a=2$，$b=-4$，$c=-1$，
$\therefore \Delta =b^{2}-4ac=\left(-4\right)^{2}-4\times 2\times \left(-1\right)=24 \gt 0$，
$\therefore x=\frac{4±\sqrt{24}}{2×2}=\frac{2±\sqrt{6}}{2}=1±\frac{\sqrt{6}}{2}$，
$\therefore {x}_{1}=1+\frac{\sqrt{6}}{2}，{x}_{2}=1-\frac{\sqrt{6}}{2}$.
解法二：$2x^{2}-4x-1=0$，
$2x^{2}-4x=1$，
$x^{2}-2x=\frac{1}{2}$，
$x^{2}-2x+1=\frac{3}{2}$，
$\therefore \left(x-1\right)^{2}=\frac{3}{2}$，
$\therefore x-1=\pm \frac{\sqrt{6}}{2}$，
$\therefore {x}_{1}=1+\frac{\sqrt{6}}{2}，{x}_{2}=1-\frac{\sqrt{6}}{2}$.