3x-6/x=x-2

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Solution for 3x-6/x=x-2 equation: 


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

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

DELTA = 52

DELTA > 0

x = (52^(1/2)-2)/(2*2) or x = (-52^(1/2)-2)/(2*2)

x = (2*13^(1/2)-2)/4 or x = (-2*13^(1/2)-2)/4

x in { (-2*13^(1/2)-2)/4, (2*13^(1/2)-2)/4} 

x in { (-2*13^(1/2)-2)/4, (2*13^(1/2)-2)/4 }

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