1/x=2x-1

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


D( x )

x = 0

x = 0

x = 0

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

1/x = 2*x-1 // - 2*x-1

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

1/x-2*x+1 = 0

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

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

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

x^1

x-2*x^2+1 = 0

x-2*x^2+1 = 0

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

DELTA = 9

DELTA > 0

x = (9^(1/2)-1)/(-2*2) or x = (-9^(1/2)-1)/(-2*2)

x = -1/2 or x = 1

x in { -1/2, 1} 

x in { -1/2, 1 }

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