\(x\left(2x-3\right)-4x^2+9=0\\ =>x\left(2x-3\right)-\left(4x^2-9\right)=0\\ =>x\left(2x-3\right)-\left(2x-3\right)\left(2x+3\right)=0\\ =>\left(2x-3\right)\left(x-2x-3\right)=0\\ =>\left[{}\begin{matrix}2x-3=0\\-x-3=0\end{matrix}\right.=>\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-3\end{matrix}\right.\)