Answer
$$x=\frac{\sqrt{89}-3}{8},\:x=\frac{-\sqrt{89}-3}{8}$$
Work Step by Step
In order to solve this problem, we use the method of completing the square. Doing this, we find:
$$ x^2+\frac{3x}{4}=\frac{5}{4}\\ x^2+\frac{3x}{4}+\left(\frac{3}{8}\right)^2=\frac{5}{4}+\left(\frac{3}{8}\right)^2\\ \left(x+\frac{3}{8}\right)^2=\frac{89}{64}\\ x=\frac{\sqrt{89}-3}{8},\:x=\frac{-\sqrt{89}-3}{8}$$