Answer
{$\dfrac{-1}{18} - \dfrac{\sqrt{71}}{18}i,\dfrac{-1}{18} + \dfrac{\sqrt{71}}{18}i$}
Work Step by Step
Quadratic formula suggests that $x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$
Since, $9x^2+x+2=0$
Thus, $x=\dfrac{-(1) \pm \sqrt{(1)^2-4(9)(2)}}{2(9)}$
or, $x=\dfrac{-1 \pm \sqrt{-71}}{18}$
or, $x=\dfrac{-1}{18} \pm \dfrac{\sqrt{71}}{18}i$
or, $x=\dfrac{-1}{18} - \dfrac{\sqrt{71}}{18}i,\dfrac{-1}{18} + \dfrac{\sqrt{71}}{18}i$
Our solution set is: {$\dfrac{-1}{18} - \dfrac{\sqrt{71}}{18}i,\dfrac{-1}{18} + \dfrac{\sqrt{71}}{18}i$}
