2x-6/x=x-4/2

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Solution for 2x-6/x=x-4/2 equation: 


D( x )

x = 0

x = 0

x = 0

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

2*x-(6/x) = x-(4/2) // - x-(4/2)

2*x-x-(6/x)+4/2 = 0

2*x-x-6*x^-1+4/2 = 0

1*x^1-6*x^-1+2*x^0 = 0

(1*x^2+2*x^1-6*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2+2*x^1-6*x^0) = 0

x^1

x^2+2*x-6 = 0

x^2+2*x-6 = 0

DELTA = 2^2-(-6*1*4)

DELTA = 28

DELTA > 0

x = (28^(1/2)-2)/(1*2) or x = (-28^(1/2)-2)/(1*2)

x = (2*7^(1/2)-2)/2 or x = (-2*7^(1/2)-2)/2

x in { (-2*7^(1/2)-2)/2, (2*7^(1/2)-2)/2} 

x in { (-2*7^(1/2)-2)/2, (2*7^(1/2)-2)/2 }

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