Answer
$$x=\frac{\sqrt{13}-3}{2},\:x=\frac{-\sqrt{13}-3}{2}$$
Work Step by Step
We complete the square to find:
$$x^2+3x-1+\left(\frac{3}{2}\right)^2-\left(\frac{3}{2}\right)^2 \\ \left(x+\frac{3}{2}\right)^2-1-\left(\frac{3}{2}\right)^2 \\ \left(x+\frac{3}{2}\right)^2-\frac{13}{4} \\ x=\frac{\sqrt{13}-3}{2},\:x=\frac{-\sqrt{13}-3}{2}$$
