\(\left(4x-1\right)^2-x\left(3-x\right)=121\)
\(\Leftrightarrow16x^2-8x+1-3x+x^2=121\)
\(\Leftrightarrow17x^2-11x-120=0\)
\(\Leftrightarrow17x^2-51x+40x-120=0\)
\(\Leftrightarrow\left(17x^2-51x\right)+\left(40x-120\right)=0\)
\(\Leftrightarrow17x\left(x-3\right)+40\left(x-3\right)=0\)
\(\Leftrightarrow\left(17x+40\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}17x+40=0\\x-3=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-40}{17}\\x=3\end{matrix}\right.\)
\(5x^2-x=18\)
\(\Leftrightarrow5x^2-x-18=0\)
\(\Leftrightarrow5x^2-10x+9x-18=0\)
\(\Leftrightarrow\left(5x^2-10x\right)+\left(9x-18\right)=0\)
\(\Leftrightarrow5x\left(x-2\right)+9\left(x-2\right)=0\)
\(\Leftrightarrow\left(5x+9\right)\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}5x+9=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-9}{5}\\x=2\end{matrix}\right.\)
