5/6=x-6/x+1

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Solution for 5/6=x-6/x+1 equation: 


D( x )

x = 0

x = 0

x = 0

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

5/6 = x-(6/x)+1 // - x-(6/x)+1

6/x-x+5/6-1 = 0

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

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

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

x^1

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

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

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

DELTA = 865/36

DELTA > 0

x = ((865/36)^(1/2)-(-1/6))/(-1*2) or x = (-(-1/6)-(865/36)^(1/2))/(-1*2)

x = ((865/36)^(1/2)+1/6)/(-2) or x = (1/6-(865/36)^(1/2))/(-2)

x in { ((865/36)^(1/2)+1/6)/(-2), (1/6-(865/36)^(1/2))/(-2)} 

x in { ((865/36)^(1/2)+1/6)/(-2), (1/6-(865/36)^(1/2))/(-2) }

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