(20-x)/x=x

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Solution for (20-x)/x=x equation: 


D( x )

x = 0

x = 0

x = 0

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

(20-x)/x = x // - x

(20-x)/x-x = 0

(20-x)/x+(-x*x)/x = 0

20-x*x-x = 0

20-x^2-x = 0

20-x^2-x = 0

20-x^2-x = 0

DELTA = (-1)^2-(-1*4*20)

DELTA = 81

DELTA > 0

x = (81^(1/2)+1)/(-1*2) or x = (1-81^(1/2))/(-1*2)

x = -5 or x = 4

(x+5)*(x-4) = 0

((x+5)*(x-4))/x = 0

((x+5)*(x-4))/x = 0 // * x

(x+5)*(x-4) = 0

( x+5 )

x+5 = 0 // - 5

x = -5

( x-4 )

x-4 = 0 // + 4

x = 4

x in { -5, 4 }

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