You can solve this equation if first in:

 

divide both sides by 5^(2x)

4 - 25*(2^2)*(2/5)^2x - 9*(2/5)^x = 0

Let t=(2/5)^x then we get the following equation:

4 - 100*t^2 - 9t = 0

click here to see the step by step solution for t

For t = 4/25 we have

(2/5)^x = 4/25

(2/5)^x = (2/5)^2

One solution is x = 2.

For t = -1/4 we have

(2/5)^x = -1/4

Since (2/5)^x i always larger than 0, for any real number 'x' follows there is no real number 'x' such that:

(2/5)^x = -1/4

Thus, the only real solution is x = 2.