(5/x-7)-(5/1-x)=0

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Solution for (5/x-7)-(5/1-x)=0 equation: 


D( x )

x = 0

x = 0

x = 0

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

x+5/x-(5/1)-7 = 0

x+5/x-7-5 = 0

1*x^1+5*x^-1-12*x^0 = 0

(1*x^2-12*x^1+5*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-12*x^1+5*x^0) = 0

x^1

x^2-12*x+5 = 0

x^2-12*x+5 = 0

DELTA = (-12)^2-(1*4*5)

DELTA = 124

DELTA > 0

x = (124^(1/2)+12)/(1*2) or x = (12-124^(1/2))/(1*2)

x = (2*31^(1/2)+12)/2 or x = (12-2*31^(1/2))/2

x in { (12-2*31^(1/2))/2, (2*31^(1/2)+12)/2} 

x in { (12-2*31^(1/2))/2, (2*31^(1/2)+12)/2 }

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