Answer
$\displaystyle =\frac{1}{3}\pm\frac{\sqrt{2}}{3}i$
Work Step by Step
We are given:
$3x^{2}-2x=-1$
$3x^{2}-2x+1=0$
We use the quadratic formula (with $a=3, b=-2, c=1$):
$\displaystyle x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$\displaystyle =\frac{-(-2)\pm\sqrt{(-2)^{2}-4(3)(1)}}{2(3)}$
$\displaystyle =\frac{2\pm\sqrt{-8}}{6}$
$\displaystyle =\frac{2\pm 2i\sqrt{2}}{6}$
$\displaystyle =\frac{1}{3}\pm\frac{\sqrt{2}}{3}i$
