Answer
$x=-\dfrac{3}{2}\pm\dfrac{\sqrt{17}}{2}$
Work Step by Step
Using the completing the square method, then,
\begin{array}{l}
x^2+3x-2=0\\
x^2+3x=2\\
x^2+3x+\left( \dfrac{3}{2} \right)^2=2+\left( \dfrac{3}{2}\right)^2\\
x^2+3x+\dfrac{9}{4}=2+\dfrac{9}{4}\\
\left( x+\dfrac{3}{2} \right)^2=\dfrac{17}{4}\\
x+\dfrac{3}{2}=\pm\sqrt{\dfrac{17}{4}}\\
x=-\dfrac{3}{2}\pm\dfrac{\sqrt{17}}{2}
.\end{array}
