2(x+2)=1/x

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Solution for 2(x+2)=1/x equation: 


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

2*x^2+4*x-1 = 0

2*x^2+4*x-1 = 0

2*x^2+4*x-1 = 0

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

DELTA = 24

DELTA > 0

x = (24^(1/2)-4)/(2*2) or x = (-24^(1/2)-4)/(2*2)

x = (2*6^(1/2)-4)/4 or x = (-2*6^(1/2)-4)/4

(x-((-2*6^(1/2)-4)/4))*(x-((2*6^(1/2)-4)/4)) = 0

((x-((-2*6^(1/2)-4)/4))*(x-((2*6^(1/2)-4)/4)))/x = 0

((x-((-2*6^(1/2)-4)/4))*(x-((2*6^(1/2)-4)/4)))/x = 0 // * x

(x-((-2*6^(1/2)-4)/4))*(x-((2*6^(1/2)-4)/4)) = 0

( x-((-2*6^(1/2)-4)/4) )

x-((-2*6^(1/2)-4)/4) = 0 // + (-2*6^(1/2)-4)/4

x = (-2*6^(1/2)-4)/4

( x-((2*6^(1/2)-4)/4) )

x-((2*6^(1/2)-4)/4) = 0 // + (2*6^(1/2)-4)/4

x = (2*6^(1/2)-4)/4

x in { (-2*6^(1/2)-4)/4, (2*6^(1/2)-4)/4 }

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