(p+5/p+11p+30)/(7p/p+8)

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Solution for (p+5/p+11p+30)/(7p/p+8) equation: 


D( p )

p = 0

(7*p)/p+8 = 0

p = 0

p = 0

(7*p)/p+8 = 0

(7*p)/p+8 = 0

15 = 0

p belongs to the empty set

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

(p+11*p+5/p+30)/((7*p)/p+8) = 0

(12*p+5*p^-1+30)/15 = 0

12*p+5*p^-1+30 = 0

12*p^1+5*p^-1+30*p^0 = 0

(12*p^2+30*p^1+5*p^0)/(p^1) = 0 // * p^2

p^1*(12*p^2+30*p^1+5*p^0) = 0

p^1

12*p^2+30*p+5 = 0

12*p^2+30*p+5 = 0

DELTA = 30^2-(4*5*12)

DELTA = 660

DELTA > 0

p = (660^(1/2)-30)/(2*12) or p = (-660^(1/2)-30)/(2*12)

p = (2*165^(1/2)-30)/24 or p = (-2*165^(1/2)-30)/24

p in { (-2*165^(1/2)-30)/24, (2*165^(1/2)-30)/24} 

(p-((-2*165^(1/2)-30)/24))*(p-((2*165^(1/2)-30)/24)) = 0

((p-((-2*165^(1/2)-30)/24))*(p-((2*165^(1/2)-30)/24)))/15 = 0

( p-((-2*165^(1/2)-30)/24) )

p-((-2*165^(1/2)-30)/24) = 0 // + (-2*165^(1/2)-30)/24

p = (-2*165^(1/2)-30)/24

( p-((2*165^(1/2)-30)/24) )

p-((2*165^(1/2)-30)/24) = 0 // + (2*165^(1/2)-30)/24

p = (2*165^(1/2)-30)/24

p in { (-2*165^(1/2)-30)/24, (2*165^(1/2)-30)/24 }

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