#### Answer

{$-1,\dfrac{-3}{5}$}

#### Work Step by Step

Quadratic formula suggests that $x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$
Given: $5x^2+8x=-3$
It can be written as: $5x^2+8x+3=0$
Thus, $x=\dfrac{-(8) \pm \sqrt{(8)^2-4(5)(3)}}{2(5)}$
or, $x=\dfrac{-8 \pm 2}{10}$
or, $x=\dfrac{-8 + 2}{10}=\dfrac{-3}{5}$ and $x=\dfrac{-8-2}{10}=-1$
Our solution set is: {$-1,\dfrac{-3}{5}$}