Answer
$x=\displaystyle \frac{1}{2}$ or $x=-\displaystyle \frac{7}{2}$
Work Step by Step
We complete the square:
$ x^{2}+3x-\displaystyle \frac{7}{4}=0$
$x^{2}+3x=\frac{7}{4}$
$x^{2}+3x+\frac{9}{4}=\frac{7}{4}+\frac{9}{4}=\frac{16}{4}=4$
$(x+\frac{3}{2})^{2}=4$
$x+\frac{3}{2}=\pm 2$
$x=-\frac{3}{2}\pm 2$
$x=\displaystyle \frac{1}{2}$ or $x=-\displaystyle \frac{7}{2}$
