(56-x)/x=x

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Solution for (56-x)/x=x equation: 


D( x )

x = 0

x = 0

x = 0

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

(56-x)/x = x // - x

(56-x)/x-x = 0

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

56-x*x-x = 0

56-x^2-x = 0

56-x^2-x = 0

56-x^2-x = 0

DELTA = (-1)^2-(-1*4*56)

DELTA = 225

DELTA > 0

x = (225^(1/2)+1)/(-1*2) or x = (1-225^(1/2))/(-1*2)

x = -8 or x = 7

(x+8)*(x-7) = 0

((x+8)*(x-7))/x = 0

((x+8)*(x-7))/x = 0 // * x

(x+8)*(x-7) = 0

( x+8 )

x+8 = 0 // - 8

x = -8

( x-7 )

x-7 = 0 // + 7

x = 7

x in { -8, 7 }

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