x/x^2-6x=1

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Solution for x/x^2-6x=1 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

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

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

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

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

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

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

x^1

1-6*x^2-x = 0

1-6*x^2-x = 0

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

DELTA = 25

DELTA > 0

x = (25^(1/2)+1)/(-6*2) or x = (1-25^(1/2))/(-6*2)

x = -1/2 or x = 1/3

x in { -1/2, 1/3} 

x in { -1/2, 1/3 }

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