Answer
The solution set in standard form is $$\Big\{-\frac{2}{3}\pm\frac{\sqrt2}{3}i\Big\}$$
Work Step by Step
$$3x^2+2=-4x$$
First, write the equation in standard form.
$$3x^2+4x+2=0$$
Now use the quadratic formula.
$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$
As $a=3, b=4, c=2$
$$x=\frac{-4\pm\sqrt{4^2-4\times3\times2}}{2\times3}$$
$$x=\frac{-4\pm\sqrt{16-24}}{6}$$
$$x=\frac{-4\pm\sqrt{-8}}{6}$$
Now we rewrite $\sqrt{-8}=i\sqrt8=2i\sqrt2$
$$x=\frac{-4\pm2i\sqrt2}{6}$$
Finally, we simplify
$$x=\frac{-2\pm i\sqrt2}{3}$$
The solution set in standard form is $$\Big\{-\frac{2}{3}\pm\frac{\sqrt2}{3}i\Big\}$$