\(\left(3x-1\right)\left(x-3\right)-9+x^2=0\)
\(\Leftrightarrow3x^2-9x-x+3-9+x^2=0\)
\(\Leftrightarrow4x^2-10x-6=0\)
\(\Leftrightarrow\) \(2\left(2x+1\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=3\end{matrix}\right.\)
Vậy \(S=\left\{-\dfrac{1}{2};3\right\}\).
\(\left(3x-1\right)\left(x-3\right)-9+x^2=0\\ \Leftrightarrow\left(3x-1\right)\left(x-3\right)+x^2-9=0\\ \Leftrightarrow\left(3x-1\right)\left(x-3\right)+\left(x-3\right)\left(x+3\right)=0\\ \Leftrightarrow\left(x-3\right)\left(3x-1+x+3\right)=0\\ \Leftrightarrow\left(x-3\right)\left(4x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-3=0\\4x+2=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\4x=-2\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{1}{2}\end{matrix}\right.\)
Vậy \(S=\left\{3;-\dfrac{1}{2}\right\}\)
