585/x=(585/(x-4))-20

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Solution for 585/x=(585/(x-4))-20 equation: 


D( x )

x = 0

x-4 = 0

x = 0

x = 0

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x in (-oo:0) U (0:4) U (4:+oo)

585/x = 585/(x-4)-20 // - 585/(x-4)-20

585/x-(585/(x-4))+20 = 0

585/x-585*(x-4)^-1+20 = 0

585/x-585/(x-4)+20 = 0

(-585*x)/(x*(x-4))+(585*(x-4))/(x*(x-4))+(20*x*(x-4))/(x*(x-4)) = 0

585*(x-4)+20*x*(x-4)-585*x = 0

20*x^2-80*x-2340 = 0

20*x^2-80*x-2340 = 0

20*(x^2-4*x-117) = 0

x^2-4*x-117 = 0

DELTA = (-4)^2-(-117*1*4)

DELTA = 484

DELTA > 0

x = (484^(1/2)+4)/(1*2) or x = (4-484^(1/2))/(1*2)

x = 13 or x = -9

20*(x+9)*(x-13) = 0

(20*(x+9)*(x-13))/(x*(x-4)) = 0

(20*(x+9)*(x-13))/(x*(x-4)) = 0 // * x*(x-4)

20*(x+9)*(x-13) = 0

( 20 )

20 = 0

x belongs to the empty set

( x+9 )

x+9 = 0 // - 9

x = -9

( x-13 )

x-13 = 0 // + 13

x = 13

x in { -9, 13 }

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