To solve this inequality, we first need to expand both sides to simplify the expression:

Left side:
(5x - 2)^2 - 15
= (5x - 2)(5x - 2) - 15
= 25x^2 - 10x - 10x + 4 - 15
= 25x^2 - 20x - 11

Right side:
(4x - 1)^2 + 9x^2
= (4x - 1)(4x - 1) + 9x^2
= 16x^2 - 4x - 4x + 1 + 9x^2
= 25x^2 - 8x + 1

Now we have the inequality:
25x^2 - 20x - 11 > 25x^2 - 8x + 1

Subtracting 25x^2 from both sides, we get:
-20x - 11 > -8x + 1

Now, we can isolate the variable x by moving all terms involving x to one side:

-20x + 8x > 1 + 11
-12x > 12

Dividing by -12 (and flipping the inequality because we are dividing by a negative number):

x < -1

So the solution to the given inequality is x < -1.