2x^2-x=2-1/x

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

x^1

2*x^3-x^2-2*x+1 = 0

{ 1, -1 }

1

x = 1

2*x^3-x^2-2*x+1 = 0

1

x-1

2*x^2+x-1

2*x^3-x^2-2*x+1

x-1

2*x^2-2*x^3

x^2-2*x+1

x-x^2

1-x

x-1

0

2*x^2+x-1 = 0

DELTA = 1^2-(-1*2*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, 1/2, 1} 

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

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