$3x^3 = 24$ quadratic equation Completing the square I know by factoring
$$x^3 - 8 = 0\\
x-2 = 0$$
that one of the solutions is 2.
but the other solutions is $1 ± i \sqrt 3$.
Can someone explain to me how to get that?

May be you know this already but it's not clear to me from your post that you have the progression from the original problem statement to the final two factors exactly correct.
$3x^3 = 24 \\ \Rightarrow 3x^3 - 24 = 0 \\ \Rightarrow 3\left(x^3 - 8\right) = 0 \\ \Rightarrow x^3 - 8 = 0 \\ \Rightarrow \left(x-2\right)\left(x^2+2x+4\right) = 0 \\
\Rightarrow x-2 = 0, \ \ x^2+2x+4 = 0$
The first factor results in $x = 2$.  The second factor must be solved using the quadratic formula or by completing the square since it is not factorable (Quadratic Formula on Wikipedia).
