p-4/p = 16/5p - 1/5

If you mean:  p - 4/p  =  16/(5p) - 1/5

Multiply each term by the lowest common denominator, 5p:

--->   5p² -20  =  16 - p

--->   5p² + p - 36  =  0

Using the quadratic formula, with a = 5, b = 1, and c = -36:

--->  p  =  [-1 ± √( (-1)² - 4(5)(-36) ] / ( 2 · 5 )

If you mean:  p - 4/p  =  (16/5)p - 1/5

Multiply each term by 5p:

--->   5p² - 20  =  16p² - p

--->   -11p² + p - 20  =  0

if you use the quadratic formula, you will not get real answers.

p = 1.8 or -2