Ta có: x(4x-5)=6
\(\Leftrightarrow4x^2-5x-6=0\)
\(\Leftrightarrow4x^2-8x+3x-6=0\)
\(\Leftrightarrow4x\left(x-2\right)+3\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(4x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\4x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\4x=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\frac{-3}{4}\end{matrix}\right.\)
Vậy: \(S=\left\{2;\frac{-3}{4}\right\}\)
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