3-(x/2)=1/x

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

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

DELTA = 7

DELTA > 0

x = (7^(1/2)-3)/(2*(-1/2)) or x = (-7^(1/2)-3)/(2*(-1/2))

x = 3-7^(1/2) or x = 7^(1/2)+3

x in { 3-7^(1/2), 7^(1/2)+3} 

x in { 3-7^(1/2), 7^(1/2)+3 }

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