#### Answer

$x=-4\pm2i$

#### Work Step by Step

$\dfrac{1}{8}x^{2}+x+\dfrac{5}{2}=0$
Multiply the whole equation by $8$ to avoid working with fractions:
$8\Big(\dfrac{1}{8}x^{2}+x+\dfrac{5}{2}=0\Big)$
$x^{2}+8x+20=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here $a=1$, $b=8$ and $c=20$.
Substitute:
$x=\dfrac{-8\pm\sqrt{8^{2}-4(1)(20)}}{2(1)}=\dfrac{-8\pm\sqrt{64-80}}{2}=...$
$...=\dfrac{-8\pm\sqrt{-16}}{2}=\dfrac{-8\pm4i}{2}=-4\pm2i$