Answer
$\left\{ \dfrac{\sqrt{3}-\sqrt{11}}{2},\dfrac{\sqrt{3}+\sqrt{11}}{2} \right\}$
Work Step by Step
Using $\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solutions of the given quadratic equation, $
2x^2-\sqrt{3}x-1=0
,$ are
\begin{array}{l}\require{cancel}
\dfrac{-(-\sqrt{3})\pm\sqrt{(-\sqrt{3})^2-4(2)(-1)}}{2(1)}
\\\\=
\dfrac{\sqrt{3}\pm\sqrt{3+8}}{2}
\\\\=
\dfrac{\sqrt{3}\pm\sqrt{11}}{2}
.\end{array}
Hence, the solutions are $
\left\{ \dfrac{\sqrt{3}-\sqrt{11}}{2},\dfrac{\sqrt{3}+\sqrt{11}}{2} \right\}
.$
