Answer
$\frac{ 3 \pm \sqrt3 }{2}$
Work Step by Step
We first get rid of all of the fractions and get everything on one side of the equation:
$2x^2 -6x = -3 \\ 2x^2 -6x + 3 = 0 $
We apply the quadratic formula:
$ x = \frac{ -b \pm \sqrt{b^2 -4ac}}{2a} \\
x = \frac{6 \pm \sqrt{(-6)^2 -4(2)(3)}}{2(2)} \
\\ x = \frac{6 \pm \sqrt{(12)}}{4} \\ x = \frac{ 3 \pm \sqrt3 }{2}$
