Question 134607
Given: {{{(x-9) = sqrt(x-3)}}}
square both sides
{{{(x-9)^2 = x -3}}}
{{{x^2 - 18x + 81 = x - 3}}}
{{{x^2 - 19x + 84 = 0}}}
{{{(x-12)(x-7)=0}}}
x =12, x =7 are potential solutions.

Test them
x = 12 ==> 12-9 = sqrt(9)  this is true so 12 works
x = 7 ==> 7-9 = sqrt(4)  generally a sqrt for this type of problem is the positive root. If the negative root is acceptable, then this works too