1/x-1=x-1/4

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Solution for 1/x-1=x-1/4 equation: 


D( x )

x = 0

x = 0

x = 0

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

1/x-1 = x-(1/4) // - x-(1/4)

1/x-x+1/4-1 = 0

1*x^-1-1*x^1-3/4*x^0 = 0

(1*x^0-1*x^2-3/4*x^1)/(x^1) = 0 // * x^2

x^1*(1*x^0-1*x^2-3/4*x^1) = 0

x^1

(-3/4)*x-x^2+1 = 0

(-3/4)*x-x^2+1 = 0

DELTA = (-3/4)^2-(-1*1*4)

DELTA = 73/16

DELTA > 0

x = ((73/16)^(1/2)-(-3/4))/(-1*2) or x = (-(-3/4)-(73/16)^(1/2))/(-1*2)

x = ((73/16)^(1/2)+3/4)/(-2) or x = (3/4-(73/16)^(1/2))/(-2)

x in { ((73/16)^(1/2)+3/4)/(-2), (3/4-(73/16)^(1/2))/(-2)} 

x in { ((73/16)^(1/2)+3/4)/(-2), (3/4-(73/16)^(1/2))/(-2) }

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