$x^{2}-7x-1=0$，
$\therefore \Delta =\left(-7\right)^{2}-4\times 1\times \left(-1\right)=53 \gt 0$，即该方程有两个不等的实数根，
$\therefore x=\frac{-(-7)±\sqrt{{(-7)}^{2}-4×1×(-1)}}{2×1}=\frac{7±\sqrt{53}}{2}$，
$\therefore {x}_{1}=\frac{7+\sqrt{53}}{2}，{x}_{2}=\frac{7-\sqrt{53}}{2}$.

$x^{2}-7x-1=0$，
$\therefore \Delta =\left(-7\right)^{2}-4\times 1\times \left(-1\right)=53 \gt 0$，即该方程有两个不等的实数根，
$\therefore x=\frac{-(-7)±\sqrt{{(-7)}^{2}-4×1×(-1)}}{2×1}=\frac{7±\sqrt{53}}{2}$，
$\therefore {x}_{1}=\frac{7+\sqrt{53}}{2}，{x}_{2}=\frac{7-\sqrt{53}}{2}$.