Answer
$\left\{\dfrac{1-\sqrt 2i}{3},\dfrac{1+\sqrt 2i}{3}\right\}$
Work Step by Step
We are given the equation:
$3x^2-2x=-1$
Rewrite the equation in standard form:
$3x^2-2x+1=0$
Use the quadratic formula:
$x=\dfrac{2\pm\sqrt{(-2)^2-4(3)(1)}}{2(3)}=\dfrac{2\pm 2\sqrt 2i}{6}=\dfrac{1\pm\sqrt 2i}{3}$
The solution set is:
$\left\{\dfrac{1-\sqrt 2i}{3},\dfrac{1+\sqrt 2i}{3}\right\}$
