#### Answer

$x=-6$
$x={\dfrac{14}{5}}$

#### Work Step by Step

$x=\dfrac{-b±{\sqrt {b^{2}-4ac}}}{2a}$ and $5x^{2}+16x-84=0$.Therefore, $a=5$,$b=16$ and $c=-84$:
Substitute the values:
$x=\dfrac{-16±{\sqrt {16^{2}-4(5)(-84)}}}{2(5)}$
=$\dfrac{-16±{\sqrt {256-(-1680)}}}{10}$
=$\dfrac{-16± {\sqrt {1936}}}{10}$
=$\dfrac{-16±44}{10}$
Separate the equation into plus and minus equations:
$x=\dfrac{-16-44}{10}=-6$
$x=\dfrac{-16+44}{10}={\dfrac{14}{5}}$