Answer
$\displaystyle x=\frac{-2\pm\sqrt{10}}{2}$
Work Step by Step
$2x(x+2)=3$
$2x^{2}+4x=3$
$2x^{2}+4x-3=0$
We solve using the quadratic formula ($a=2,\ b=4,\ c=-3$):
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$\displaystyle x=\displaystyle \frac{-4\pm\sqrt{4^{2}-4*2*-3}}{2*2}$
$\displaystyle x=\frac{-4\pm\sqrt{16+24}}{4}$
$\displaystyle x=\frac{-4\pm\sqrt{40}}{4}$
$\displaystyle x=\frac{-4\pm\sqrt{4*10}}{4}$
$\displaystyle x=\frac{-4\pm 2\sqrt{10}}{4}$
$\displaystyle x=\frac{-2\pm\sqrt{10}}{2}$
