\(3x-24+3x^2=0\\ \Leftrightarrow x^2+x-8=0 \)
\(\Delta=1^2-4.\left(-8\right)=1+32=33\)
\(\Rightarrow\left\{{}\begin{matrix}x_1=\dfrac{-1-\sqrt{33}}{2}\\x_2=\dfrac{-1+\sqrt{33}}{2}\end{matrix}\right.\)
\(\Leftrightarrow x^2+x-8=0\)
\(\Leftrightarrow x^2+x+\dfrac{1}{4}-\dfrac{33}{4}=0\)
\(\Leftrightarrow\left(x+\dfrac{1}{2}\right)^2=\dfrac{33}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{\sqrt{33}}{2}\\x+\dfrac{1}{2}=-\dfrac{\sqrt{33}}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\sqrt{33}-1}{2}\\x=\dfrac{-\sqrt{33}-1}{2}\end{matrix}\right.\)
