Simplify 3x² + 2x + 6 =0

$$x = \frac{-2 \pm \sqrt{4 - 72}}{6}$$ $$x = \frac{-2 \pm \sqrt{-68}}{6}$$

We can write $\sqrt{-68}$ as $\sqrt{68}i$, where $i$ is the imaginary unit ($i = \sqrt{-1}$).

$$x = \frac{-2 \pm \sqrt{68}i}{6}$$

Since $68 = 4 \times 17$, we have $\sqrt{68} = \sqrt{4 \times 17} = 2\sqrt{17}$.

$$x = \frac{-2 \pm 2\sqrt{17}i}{6}$$

$$x = \frac{-2}{6} \pm \frac{2\sqrt{17}i}{6}$$ $$x = -\frac{1}{3} \pm \frac{\sqrt{17}}{3}i$$

The solutions are complex numbers.

The simplified form of the equation is:

$$x = -\frac{1}{3} \pm \frac{\sqrt{17}}{3}i$$