Answer
{$-\frac{5}{2},3$}
Work Step by Step
$2x^{2}-x-15=0$
$2x^{2}-6x+5x-15=0$
$2x(x-3)+5(x-3)=0$
$(x-3)(2x+5)=0$
$(x-3)=0$ or $(2x+5)=0$
$x=3$ or $x=-\frac{5}{2}$
Check:
Substituting $x=3$ in the equation,
$2(3)^{2}-3-15=0$
$18-3-15=0$
$18-18=0$
$0=0$
Substituting $x=-\frac{5}{2}$ in the equation,
$2(-\frac{5}{2})^{2}-(-\frac{5}{2})-15=0$
$\frac{50}{4}+\frac{5}{2}-15=0$
$\frac{25}{2}+\frac{5}{2}-15=0$
$\frac{30}{2}-15=0$
$15-15=0$
$0=0$
Both values check and the solution set is {$-\frac{5}{2},3$}
