1200/p-80=p

Solution for 1200/p-80=p equation:

D( p )

p = 0

p = 0

p = 0

p in (-oo:0) U (0:+oo)

1200/p-80 = p // - p

1200/p-p-80 = 0

1200*p^-1-1*p^1-80*p^0 = 0

(1200*p^0-1*p^2-80*p^1)/(p^1) = 0 // * p^2

p^1*(1200*p^0-1*p^2-80*p^1) = 0

p^1

1200-p^2-80*p = 0

1200-p^2-80*p = 0

DELTA = (-80)^2-(-1*4*1200)

DELTA = 11200

DELTA > 0

p = (11200^(1/2)+80)/(-1*2) or p = (80-11200^(1/2))/(-1*2)

p = (40*7^(1/2)+80)/(-2) or p = (80-40*7^(1/2))/(-2)

p in { (40*7^(1/2)+80)/(-2), (80-40*7^(1/2))/(-2)} 

p in { (40*7^(1/2)+80)/(-2), (80-40*7^(1/2))/(-2) }