6.3.1. (12 points) Solve the equation $2 x^{3}+24 x=3-12 x^{2}$.

Answer: $\sqrt[3]{\frac{19}{2}}-2 \approx 0.12$.
Solution. $2 x^{3}+24 x=3-12 x^{2} \Leftrightarrow 2\left(x^{3}+6 x^{2}+12 x+8\right)-16-3=0 \Leftrightarrow(x+2)^{3}=\frac{19}{2} \Leftrightarrow x=\sqrt[3]{\frac{19}{2}}-2$.