What is the solution for x if x = 13*square root x - 36?

We'll move all terms to one
side:

x - 13*sqrt x + 36 =
0

Let sqrt x = t

If we'll
raise to square both sides, we'll get:

x =
t^2

We'll re-write the equation in
t:

t^2 - 13t + 36 = 0

Since
the sum is 13 and the product is 36, the roots of the quadratic are t1 = 4 and t2 =
9.

But sqrt x = t1 => sqrt x = 4 => x1 =
4^2

x1 = 16

sqrt x = t2
=> sqrt x = 9 => x2 = 9^2

x2 =
81

The solutions of the given equation are:
{16 ; 81}.