√x+√(x-6)=12

√x+√(x-6)=12      subtract √x from both sides

√(x-6) = 12 - √x    square both sides

x-6  = x - 24√x + 144    subtract x-6 from both sides

0 = -24√x + 150         add 24√x to both sides

24√x = 150                divide both sides by 24

√x = 150/24 

√x = 25/4                  square both sides

x = 625/16 = 39.0625     this solution is correct.....see a graph of the solution, here.....https://www.desmos.com/calculator/pswceupknz