To solve this equation, we'll start by simplifying each square root term:

√4x + 20 = 2√x + 5 - 1/2√9x + 45 = 4

√4x = 2√x - 1/2√9x + 25

Now, let's simplify the square roots further:

2√x + 20 = 2√x - 1/2√3x + 25

Next, let's isolate the terms with square roots on one side of the equation:

2√x - 2√x + 1/2√3x = 25 - 20

1/2√3x = 5

Now, let's square both sides of the equation to eliminate the square root:

(1/2√3x)^2 = 5^2

1/4 * 3x = 25

3x/4 = 25

Now, let's solve for x:

3x = 4 * 25

3x = 100

x = 100/3

Therefore, the solution to the equation is x = 100/3.