#### Answer

$x=-\dfrac{1}{18}\pm\dfrac{\sqrt{71}}{18}i$

#### Work Step by Step

$9x^{2}+x+2=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=9$, $b=1$ and $c=2$
Substitute:
$x=\dfrac{-1\pm\sqrt{1^{2}-4(9)(2)}}{2(9)}=\dfrac{-1\pm\sqrt{1-72}}{18}=...$
$...=\dfrac{-1\pm\sqrt{-71}}{18}=\dfrac{-1\pm\sqrt{71}i}{18}=-\dfrac{1}{18}\pm\dfrac{\sqrt{71}}{18}i$