**Answer is -7/9**

5 (tan^{2}x - cos^{2}x) = 2cos2x +9

5 ( (sec^{2}x - 1) - cos^{2}x) = 2(2cos^{2}x - 1) +9

5 (1/cos^{2}x - 1- cos^{2}x) = 4cos^{2}x - 2 + 9

5 (1 - cos^{2}x - cos^{4}x ) = 4cos^{4}x + 7cos^{2}x

You solve this we get = 9cos^{4}x+12cos^{2}x-5

Therefore let cos^{4}x =y^{2} and cos^{2}x = y.

0=9y^{2} + 12y - 5

You will get the answer by solving for y