-(8/x-5)=-(x-2/4x-20)+(10/x-5)

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Solution for -(8/x-5)=-(x-2/4x-20)+(10/x-5) equation: 


D( x )

x = 0

x = 0

x = 0

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

-(8/x-5) = (2/4)*x-x+10/x-5+20 // - (2/4)*x-x+10/x-5+20

x-((2/4)*x)-(8/x)-(10/x)-20+5+5 = 0

x+(-1/2)*x-8*x^-1-10*x^-1-20+5+5 = 0

1/2*x^1-18*x^-1-10*x^0 = 0

(1/2*x^2-10*x^1-18*x^0)/(x^1) = 0 // * x^2

x^1*(1/2*x^2-10*x^1-18*x^0) = 0

x^1

(1/2)*x^2-10*x-18 = 0

(1/2)*x^2-10*x-18 = 0

DELTA = (-10)^2-(-18*4*(1/2))

DELTA = 136

DELTA > 0

x = (136^(1/2)+10)/(2*(1/2)) or x = (10-136^(1/2))/(2*(1/2))

x = 2*34^(1/2)+10 or x = 10-2*34^(1/2)

x in { 10-2*34^(1/2), 2*34^(1/2)+10} 

x in { 10-2*34^(1/2), 2*34^(1/2)+10 }

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