Answer
$x=-5 \text{ or } x=\frac{1}{2}$
Work Step by Step
There is a need to factor the trinomial on the left side of the equation.
The product of the leading term (2) and the constant term (-5) is $-10$.
The factors of $-10$ whose sum is equal to the coefficient of the middle term, which is 9, are $10$ and $-1$.
Write the middle using these factors to have:
$\\2x^2+10x-x-5=0$
Regroup to have:
$\\(2x^2+10x)+(-x-5)=0$
Factor out the GCF of each group to have:
$\\2x(x+5)+(-1)(x+5)=0
\\(x+5)(2x-1)=0$
Equate each factor to zero then solve each equation to have:
$\\x+5=0 \text{ or } 2x-1=0
\\x=-5 \text{ or } 2x=1
\\x=-5 \text{ or } x=\frac{1}{2}$
