The required values of x are x = {9, 36}.

Given

$\rm x^{2} - 45 x + 324 = 0$

$\rm or, x^{2} - (36 + 9) x + 324 = 0$

$\rm or, x^{2} - 36 x- 9x + 324 = 0$

$\rm or, x (x - 36) - 9 (x - 36) = 0$

$\rm or, (x - 9)(x - 36) = 0$

Either

$\rm (x - 9) = 0$

$\rm \therefore x = 9$

Or

$\rm (x - 36) = 0$

$\rm \therefore x = 36$