Answer
$$x=\frac{\sqrt{13}-1}{4},\:x=\frac{-\sqrt{13}-1}{4}$$
Work Step by Step
To find the x-intercepts, we set the equation equal to zero and then complete the square. Doing this, we find:
$$ x^2+\frac{x}{2}=\frac{3}{4}\\ x^2+\frac{x}{2}+\left(\frac{1}{4}\right)^2=\frac{3}{4}+\left(\frac{1}{4}\right)^2\\ \left(x+\frac{1}{4}\right)^2=\frac{13}{16}\\ x=\frac{\sqrt{13}-1}{4},\:x=\frac{-\sqrt{13}-1}{4}$$
