\(\left(x-1\right)\left(2x-1\right)=9-x\)
\(\Leftrightarrow2x^3-3x+1=9-x\)
\(\Leftrightarrow2x^2-3x+1=9-x+x\)
\(\Leftrightarrow2x^2+2x+1=9\)
\(\Leftrightarrow2x^2-2x+1-9=9-9\)
\(\Leftrightarrow2x^2-2x-8=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-\left(-2\right)+\sqrt{\left(-2\right)^2-4.2\left(-8\right)}}{2.2}\\x=\dfrac{-\left(2\right)+\sqrt{\left(-2\right)^2-4.\left(-8\right)}}{2.2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1+\sqrt{17}}{2}\\\dfrac{1-\sqrt{17}}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1+\sqrt{17}}{2}\\x=\dfrac{1-\sqrt{17}}{2}\end{matrix}\right.\)