1) (5x+9)^2 - 2x = -14

Expanding the left side:
25x^2 + 90x + 81 - 2x = -14

Rearranging terms:
25x^2 + 88x + 95 = 0

This is a quadratic equation that does not have integer solutions.
You can solve this using the quadratic formula or a graphing calculator.

2) 15x = 7(3-x) - 3

Expanding the right side:
15x = 21 - 7x - 3

Combining like terms:
15x = 18 - 7x

Adding 7x to both sides:
22x = 18

Dividing by 22 to solve for x:
x = 18/22
x = 9/11

Therefore, the solution to the second equation is x = 9/11.