Answer
$\left\{ \dfrac{-1-i\sqrt{71}}{18},\dfrac{-1+i\sqrt{71}}{18} \right\}$
Work Step by Step
The standard form of the given equation, $
2=-9x^2-x
,$ is
\begin{array}{l}\require{cancel}
9x^2+x+2=0
.\end{array}
Using $\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solutions of the quadratic equation, $
9x^2+x+2=0
,$ are
\begin{array}{l}\require{cancel}
\dfrac{-(1)\pm\sqrt{(1)^2-4(9)(2)}}{2(9)}
\\\\=
\dfrac{-1\pm\sqrt{1-72}}{18}
\\\\=
\dfrac{-1\pm\sqrt{-71}}{18}
\\\\=
\dfrac{-1\pm\sqrt{-1}\sqrt{71}}{18}
\\\\=
\dfrac{-1\pm i\sqrt{71}}{18}
.\end{array}
Hence, the solutions are $
\left\{ \dfrac{-1-i\sqrt{71}}{18},\dfrac{-1+i\sqrt{71}}{18} \right\}
.$
