(x-2)/2=6/x

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Solution for (x-2)/2=6/x equation:


D( x )

x = 0

x = 0

x = 0

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

(x-2)/2 = 6/x // - 6/x

(x-2)/2-(6/x) = 0

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

(x-2)/2-6/x = 0

(x*(x-2))/(2*x)+(-6*2)/(2*x) = 0

x*(x-2)-6*2 = 0

x^2-2*x-12 = 0

x^2-2*x-12 = 0

x^2-2*x-12 = 0

DELTA = (-2)^2-(-12*1*4)

DELTA = 52

DELTA > 0

x = (52^(1/2)+2)/(1*2) or x = (2-52^(1/2))/(1*2)

x = (2*13^(1/2)+2)/2 or x = (2-2*13^(1/2))/2

(x-((2-2*13^(1/2))/2))*(x-((2*13^(1/2)+2)/2)) = 0

((x-((2-2*13^(1/2))/2))*(x-((2*13^(1/2)+2)/2)))/(2*x) = 0

((x-((2-2*13^(1/2))/2))*(x-((2*13^(1/2)+2)/2)))/(2*x) = 0 // * 2*x

(x-((2-2*13^(1/2))/2))*(x-((2*13^(1/2)+2)/2)) = 0

( x-((2*13^(1/2)+2)/2) )

x-((2*13^(1/2)+2)/2) = 0 // + (2*13^(1/2)+2)/2

x = (2*13^(1/2)+2)/2

( x-((2-2*13^(1/2))/2) )

x-((2-2*13^(1/2))/2) = 0 // + (2-2*13^(1/2))/2

x = (2-2*13^(1/2))/2

x in { (2*13^(1/2)+2)/2, (2-2*13^(1/2))/2 }

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