(4/x-2)=(-5/x+5)+(19/x-2*x+5)

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Solution for (4/x-2)=(-5/x+5)+(19/x-2*x+5) equation: 


D( x )

x = 0

x = 0

x = 0

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

4/x-2 = 19/x-(2*x)-5/x+5+5 // - 19/x-(2*x)-5/x+5+5

2*x+4/x-(-5/x)-(19/x)-5-5-2 = 0

2*x+4/x+5*x^-1-19*x^-1-5-5-2 = 0

2*x^1-10*x^-1-12*x^0 = 0

(2*x^2-12*x^1-10*x^0)/(x^1) = 0 // * x^2

x^1*(2*x^2-12*x^1-10*x^0) = 0

x^1

2*x^2-12*x-10 = 0

2*x^2-12*x-10 = 0

DELTA = (-12)^2-(-10*2*4)

DELTA = 224

DELTA > 0

x = (224^(1/2)+12)/(2*2) or x = (12-224^(1/2))/(2*2)

x = (4*14^(1/2)+12)/4 or x = (12-4*14^(1/2))/4

x in { (12-4*14^(1/2))/4, (4*14^(1/2)+12)/4} 

x in { (12-4*14^(1/2))/4, (4*14^(1/2)+12)/4 }

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