$\left(1\right)x^{2}-3x=4$，
整理，得：$x^{2}-3x-4=0$，
$(x-4)\left(x+1\right)=0$，
$\therefore x-4=0$或$x+1=0$，
解得$x_{1}=4$，$x_{2}=-1$；

$(2)\because 2\left(x-3\right)=x^{2}-9$，
$\therefore 2\left(x-3\right)-\left(x+3\right)\left(x-3\right)=0$，
则$\left(x-3\right)\left(-x-1\right)=0$，
$\therefore x-3=0$或$-x-1=0$，
解得$x_{1}=3$，$x_{2}=-1$.

$\left(1\right)x^{2}-3x=4$，
整理，得：$x^{2}-3x-4=0$，
$(x-4)\left(x+1\right)=0$，
$\therefore x-4=0$或$x+1=0$，
解得$x_{1}=4$，$x_{2}=-1$；

$(2)\because 2\left(x-3\right)=x^{2}-9$，
$\therefore 2\left(x-3\right)-\left(x+3\right)\left(x-3\right)=0$，
则$\left(x-3\right)\left(-x-1\right)=0$，
$\therefore x-3=0$或$-x-1=0$，
解得$x_{1}=3$，$x_{2}=-1$.