#### Answer

$x=\left\{ \dfrac{\sqrt{5}-3}{2},\dfrac{\sqrt{5}+3}{2} \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
x^2-\sqrt{5}x-1=0
,$ use the Quadratic Formula.
$\bf{\text{Solution Details:}}$
In the equation above, $a=
1
,$ $b=
-\sqrt{5}
,$ and $c=
-1
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{array}{l}\require{cancel}
x=\dfrac{-(-\sqrt{5})\pm\sqrt{(-\sqrt{5})^2-4(1)(-1)}}{2(1)}
\\\\
x=\dfrac{\sqrt{5}\pm\sqrt{5+4}}{2}
\\\\
x=\dfrac{\sqrt{5}\pm\sqrt{9}}{2}
\\\\
x=\dfrac{\sqrt{5}\pm3}{2}
.\end{array}
The solutions are $
x=\left\{ \dfrac{\sqrt{5}-3}{2},\dfrac{\sqrt{5}+3}{2} \right\}
.$