(2x)-3=(1/x)

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Solution for (2x)-3=(1/x) equation: 


D( x )

x = 0

x = 0

x = 0

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

2*x-3 = 1/x // - 1/x

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

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

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

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

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

x^1

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

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

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

DELTA = 17

DELTA > 0

x = (17^(1/2)+3)/(2*2) or x = (3-17^(1/2))/(2*2)

x = (17^(1/2)+3)/4 or x = (3-17^(1/2))/4

x in { (3-17^(1/2))/4, (17^(1/2)+3)/4} 

x in { (3-17^(1/2))/4, (17^(1/2)+3)/4 }

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