9x - 1 > 14x2
Rearrange the inequality
14x2 - 9x + 1 < 0
14x2 - 7x - 2x + 1 < 0
7x(2x - 1) - 1(2x - 1) < 0
(7x - 1)(2x - 1) < 0
x < 17 or 12
Final answer is 17 < x < 12 (after testing)