Answer
Solution set = $\displaystyle \{\frac{1-\sqrt{29}}{4}, \displaystyle \frac{1+\sqrt{29}}{4}\}.$
Work Step by Step
Quadratic formula: $\displaystyle \quad x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
Add $-2x-7$ to both sides, so we have $ax^{2}+bx+c=0.$
$ 4x^{2}-2x-7=0\quad\rightarrow \left\{\begin{array}{l}
a=4\\
b=-2\\
c=-7
\end{array}\right.$
$x=\displaystyle \frac{2\pm\sqrt{(-2)^{2}-4(4)(-7)}}{2(4)}=\frac{2\pm\sqrt{4+112}}{8}=\frac{2\pm\sqrt{116}}{8}$
$=\displaystyle \frac{2\pm\sqrt{4\cdot 29}}{8}=\frac{2\pm 2\sqrt{29}}{8}=\frac{2(1\pm\sqrt{29})}{8}$
$=\displaystyle \frac{1\pm\sqrt{29}}{4}$
Solution set = $\displaystyle \{\frac{1-\sqrt{29}}{4}, \displaystyle \frac{1+\sqrt{29}}{4}\}.$
