#### Answer

The solutions are $x=3$ and $x=-\dfrac{5}{2}$

#### Work Step by Step

$2x^{2}-x-15=0$
Factor the left side of the equation:
$(2x+5)(x-3)=0$
Using the zero-factor property, set both factors equal to $0$ and solve each individual equation for $x$:
$2x+5=0$
$2x=-5$
$x=-\dfrac{5}{2}$
$x-3=0$
$x=3$
The solutions are $x=3$ and $x=-\dfrac{5}{2}$