8/n - 9n/16 = 1/8
Solve for n
Solve for n over the real numbers:
8/n-(9 n)/16 = 1/8
Bring 8/n-(9 n)/16 together using the common denominator 16 n:
(128-9 n^2)/(16 n) = 1/8
Cross multiply:
8 (128-9 n^2) = 16 n
Expand out terms of the left hand side:
1024-72 n^2 = 16 n
Subtract 16 n from both sides:
-72 n^2-16 n+1024 = 0
Divide both sides by -72:
n^2+(2 n)/9-128/9 = 0
Add 128/9 to both sides:
n^2+(2 n)/9 = 128/9
Add 1/81 to both sides:
n^2+(2 n)/9+1/81 = 1153/81
Write the left hand side as a square:
(n+1/9)^2 = 1153/81
Take the square root of both sides:
n+1/9 = sqrt(1153)/9 or n+1/9 = -sqrt(1153)/9
Subtract 1/9 from both sides:
n = sqrt(1153)/9-1/9 or n+1/9 = -sqrt(1153)/9
Subtract 1/9 from both sides:
Answer: |
| n = sqrt(1153)/9-1/9 or n = -1/9-sqrt(1153)/9
