5/(x-1)=x

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Solution for 5/(x-1)=x equation: 


D( x )

x-1 = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:1) U (1:+oo)

5/(x-1) = x // - x

5/(x-1)-x = 0

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

5-x*(x-1) = 0

x-x^2+5 = 0

x-x^2+5 = 0

x-x^2+5 = 0

DELTA = 1^2-(-1*4*5)

DELTA = 21

DELTA > 0

x = (21^(1/2)-1)/(-1*2) or x = (-21^(1/2)-1)/(-1*2)

x = (21^(1/2)-1)/(-2) or x = (21^(1/2)+1)/2

(x-((21^(1/2)-1)/(-2)))*(x-((21^(1/2)+1)/2)) = 0

((x-((21^(1/2)-1)/(-2)))*(x-((21^(1/2)+1)/2)))/(x-1) = 0

((x-((21^(1/2)-1)/(-2)))*(x-((21^(1/2)+1)/2)))/(x-1) = 0 // * x-1

(x-((21^(1/2)-1)/(-2)))*(x-((21^(1/2)+1)/2)) = 0

( x-((21^(1/2)+1)/2) )

x-((21^(1/2)+1)/2) = 0 // + (21^(1/2)+1)/2

x = (21^(1/2)+1)/2

( x-((21^(1/2)-1)/(-2)) )

x-((21^(1/2)-1)/(-2)) = 0 // + (21^(1/2)-1)/(-2)

x = (21^(1/2)-1)/(-2)

x in { (21^(1/2)+1)/2, (21^(1/2)-1)/(-2) }

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