4.5/x=(8-x)/(x-8)

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Solution for 4.5/x=(8-x)/(x-8) equation: 


D( x )

x = 0

x-8 = 0

x = 0

x = 0

x-8 = 0

x-8 = 0

x-8 = 0 // + 8

x = 8

x in (-oo:0) U (0:8) U (8:+oo)

4.5/x = (8-x)/(x-8) // - (8-x)/(x-8)

4.5/x-((8-x)/(x-8)) = 0

(-1*(8-x))/(x-8)+4.5/x = 0

(-1*x*(8-x))/(x*(x-8))+(4.5*(x-8))/(x*(x-8)) = 0

4.5*(x-8)-1*x*(8-x) = 0

x^2-3.5*x-36 = 0

x^2-3.5*x-36 = 0

x^2-3.5*x-36 = 0

DELTA = (-3.5)^2-(-36*1*4)

DELTA = 3.5^2+144

DELTA = 156.25

DELTA > 0

x = ((3.5^2+144)^(1/2)+3.5)/(1*2) or x = (3.5-(3.5^2+144)^(1/2))/(1*2)

x = ((3.5^2+144)^(1/2)+3.5)/2 or x = (3.5-(3.5^2+144)^(1/2))/2

(x-((3.5-(3.5^2+144)^(1/2))/2))*(x-(((3.5^2+144)^(1/2)+3.5)/2)) = 0

((x-((3.5-(3.5^2+144)^(1/2))/2))*(x-(((3.5^2+144)^(1/2)+3.5)/2)))/(x*(x-8)) = 0

((x-((3.5-(3.5^2+144)^(1/2))/2))*(x-(((3.5^2+144)^(1/2)+3.5)/2)))/(x*(x-8)) = 0 // * x*(x-8)

(x-((3.5-(3.5^2+144)^(1/2))/2))*(x-(((3.5^2+144)^(1/2)+3.5)/2)) = 0

( x-(((3.5^2+144)^(1/2)+3.5)/2) )

x-(((3.5^2+144)^(1/2)+3.5)/2) = 0 // + ((3.5^2+144)^(1/2)+3.5)/2

x = ((3.5^2+144)^(1/2)+3.5)/2

( x-((3.5-(3.5^2+144)^(1/2))/2) )

x-((3.5-(3.5^2+144)^(1/2))/2) = 0 // + (3.5-(3.5^2+144)^(1/2))/2

x = (3.5-(3.5^2+144)^(1/2))/2

x in { ((3.5^2+144)^(1/2)+3.5)/2} 

x = (3.5-(3.5^2+144)^(1/2))/2

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