Answer
$x=-3/2$ or $x=1/2$
Work Step by Step
We complete the square:
$x^{2}+x-\displaystyle \frac{3}{4}=0$
$x^{2}+x=\frac{3}{4}$
$x^{2}+x+\frac{1}{4}=\frac{3}{4}+\frac{1}{4}=1$
$(x+\frac{1}{2})^{2}=1$
$x+\frac{1}{2}=\pm 1$
$x=-\frac{1}{2}\pm 1$
So the two solutions are:
$x=-\displaystyle \frac{1}{2}-1=-\frac{3}{2}$
And:
$x=-\displaystyle \frac{1}{2}+1=\frac{1}{2}$