1/x=x/6-5/6

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

(5/6*x^1-1/6*x^2+1*x^0)/(x^1) = 0 // * x^2

x^1*(5/6*x^1-1/6*x^2+1*x^0) = 0

x^1

(-1/6)*x^2+(5/6)*x+1 = 0

(-1/6)*x^2+(5/6)*x+1 = 0

DELTA = (5/6)^2-(1*4*(-1/6))

DELTA = 49/36

DELTA > 0

x = ((49/36)^(1/2)-(5/6))/(2*(-1/6)) or x = (-(5/6)-(49/36)^(1/2))/(2*(-1/6))

x = -1 or x = 6

x in { -1, 6} 

x in { -1, 6 }

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