Answer
Solution set = $\displaystyle \{\frac{3-\sqrt{65}}{4},\frac{3+\sqrt{65}}{4}\}$
Work Step by Step
Multiply the LHS, use FOIL
$2x^{2}+2x-5x-5=2$
$2x^{2}-3x-7=0$
... apply the quadratic formula,
$ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a},\quad \left\{\begin{array}{l}
a=2\\
b=-3\\
c=-7
\end{array}\right.$
$x=\displaystyle \frac{3\pm\sqrt{(-3)^{2}-4(2)(-7)}}{2(2)}=\frac{3\pm\sqrt{9+56}}{4}=\frac{3\pm\sqrt{65}}{4}$
Solution set = $\displaystyle \{\frac{3-\sqrt{65}}{4},\frac{3+\sqrt{65}}{4}\}$
