Answer
The solution set is $\left\{-\frac{3}{2}, \frac{3}{2}\right\}$.
Work Step by Step
Add $-9$ to both sides to obtain:
$4x^2-9=0
\\(2x)^2-3^2=0$
RECALL:
A difference of two squares can be factored using the formula:
$a^2-b^2=(a-b)(a+b)$
Factor the difference of two squares to obtain:
$(2x-3)(2x+3)=0$
Equate each factor to 0, and then solve each equation to obtain:
$2x-3=0 \text{ or } 2x+3 = 0
\\2x=3 \text{ or } 2x=-3
\\x=\frac{3}{2} \text{ or } x=-\frac{3}{2}$
The solution set is $\left\{-\frac{3}{2}, \frac{3}{2}\right\}$.
