p-3-(3/5p)=(2p-3)/(5p)

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Solution for p-3-(3/5p)=(2p-3)/(5p) equation:


D( p )

5*p = 0

5*p = 0

5*p = 0

5*p = 0 // : 5

p = 0

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

p-((3/5)*p)-3 = (2*p-3)/(5*p) // - (2*p-3)/(5*p)

p-((2*p-3)/(5*p))-((3/5)*p)-3 = 0

p-((2*p-3)/(5*p))+(-3/5)*p-3 = 0

(-1*(2*p-3))/(5*p)+p+(-3*p)/5-3 = 0

(-1*5*(2*p-3))/(5*5*p)+(5*5*p*p)/(5*5*p)+(-3*5*p*p)/(5*5*p)+(-3*5*5*p)/(5*5*p) = 0

5*5*p*p-1*5*(2*p-3)-3*5*p*p-3*5*5*p = 0

25*p^2-15*p^2-10*p-75*p+15 = 0

10*p^2-10*p-75*p+15 = 0

10*p^2-85*p+15 = 0

10*p^2-85*p+15 = 0

5*(2*p^2-17*p+3) = 0

2*p^2-17*p+3 = 0

DELTA = (-17)^2-(2*3*4)

DELTA = 265

DELTA > 0

p = (265^(1/2)+17)/(2*2) or p = (17-265^(1/2))/(2*2)

p = (265^(1/2)+17)/4 or p = (17-265^(1/2))/4

5*(p-((17-265^(1/2))/4))*(p-((265^(1/2)+17)/4)) = 0

(5*(p-((17-265^(1/2))/4))*(p-((265^(1/2)+17)/4)))/(5*5*p) = 0

(5*(p-((17-265^(1/2))/4))*(p-((265^(1/2)+17)/4)))/(5*5*p) = 0 // * 5*5*p

5*(p-((17-265^(1/2))/4))*(p-((265^(1/2)+17)/4)) = 0

( p-((17-265^(1/2))/4) )

p-((17-265^(1/2))/4) = 0 // + (17-265^(1/2))/4

p = (17-265^(1/2))/4

( p-((265^(1/2)+17)/4) )

p-((265^(1/2)+17)/4) = 0 // + (265^(1/2)+17)/4

p = (265^(1/2)+17)/4

p in { (17-265^(1/2))/4, (265^(1/2)+17)/4 }

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