Question 412280
I am not sure if I understood how you set this up, I did:

N - (1/N  + 1/7)  = 9/N  

N^2  -1   N/7   = 9


7N^2  + N  -70   = 0

From here I used the quadratic equation.

N = (-1   +, -   sqrt(1  - 4(7)(-70))/14   

= -1  +, -  sqrt(1 + 1960)  / 14

(-1 +  44.28)/ 14
(-1 -  44.28)/ 14

N = 3.09,  N =-3.23  

Check 

(3.09)^2 -1  + (3.09/7)   = 9

9.5481 - 1  + .4414  =  8.9895