Question 198474
There is probably more than one way to solve this, but the easiest way is actually quite easy and I am sure you will understand it once we are done.  
First, notice that the first term is {{{(1+sqrt(x))^2}}} and the second term is {{{-2*(1+sqrt(x))}}}
Now, select any variable to replace {{{1+sqrt(x)}}} let's say z
so now substitute z for {{{1+sqrt(x)}}} and you get a problem that you better understand which is {{{z^2-2z-15=0}}}

Now you can factor the problem to factors of 15 that subtract and give you -2 which are -5 and 2
so you get {{{(z-5)(z+2)=0}}} which means either z-5=0 or z+2=0
so z=5 or z=-2

Substitute {{{1+sqrt(x)}}} for z and you get:
{{{1+sqrt(x)=5}}} and {{{1+sqrt(x)=-2}}}
{{{sqrt(x)=4}}} and {{{sqrt(x)=-3}}}
square both sides and you get
x=16 and x=9

check your answers by plugging in your answers
1.  {{{(1+sqrt(16))^2-2(1+sqrt(16))-15=0}}}
{{{(1+4)^2-2(5)-15=0}}}
{{{25-10-15=0}}}  0=0 so 16 does work!

2.{{{(1+sqrt(9))^2-2(1+sqrt(9))-15=0}}}
{{{(1+3)^2-2(1+3)-15=0}}}
{{{16-8-15=0}}} -7 does not equal 0 so 9 does not work.  Therefore, your only real answer is x=16

I hope this helps!