Solve this

Given :

$x^{2}=18 x-77$

$\Rightarrow x^{2}-18 x+77=0$

$\Rightarrow x^{2}-(11 x+7 x)+77=0$

$\Rightarrow x^{2}-11 x-7 x+77=0$

$\Rightarrow x(x-11)-7(x-11)=0$

$\Rightarrow(x-7)(x-11)=0$

$\Rightarrow x-7=0$ or $x-11=0$

$\Rightarrow x=7$ or $x=11$

Hence, 7 and 11 are the roots of the equation $x^{2}=18 x-77$.