Answer
$\displaystyle x=\frac{-3\pm 2\sqrt{3}}{3}$
Work Step by Step
$3x(x+2)=1$
$3x^{2}+6x=1$
$3x^{2}+6x-1=0$
We solve using the quadratic formula ($a=3,\ b=6,\ c=-1$):
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$\displaystyle x=\frac{-6\pm\sqrt{6^{2}-4*3*-1}}{2*3}$
$\displaystyle x=\frac{-6\pm\sqrt{36+12}}{6}$
$\displaystyle x=\frac{-6\pm\sqrt{48}}{6}$
$\displaystyle x=\frac{-6\pm\sqrt{16*3}}{6}$
$\displaystyle x=\frac{-6\pm 4\sqrt{3}}{6}$
$\displaystyle x=\frac{-3\pm 2\sqrt{3}}{3}$
