\(3x^3-7x^2+4=0\)
\(\Leftrightarrow3x^3-3x^2-4x^2+4=0\)
\(\Leftrightarrow3x^2\left(x-1\right)-4\left(x^2-1\right)=0\)
\(\Leftrightarrow3x^2\left(x-1\right)-4\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[3x^2-4\left(x+1\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(3x^2-4x-4\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(3x^2-6x+2x-4\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[3x\left(x-2\right)+2\left(x-2\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)\left(3x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-2=0\\3x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\\x=\frac{-2}{3}\end{matrix}\right.\)
Vậy \(S=\left\{1;2;\frac{-2}{3}\right\}\)