6/x=8(x-100)

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Solution for 6/x=8(x-100) equation: 


D( x )

x = 0

x = 0

x = 0

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

6/x = 8*(x-100) // - 8*(x-100)

6/x-(8*(x-100)) = 0

6/x-8*(x-100) = 0

(-8*x*(x-100))/x+6/x = 0

6-8*x*(x-100) = 0

800*x-8*x^2+6 = 0

800*x-8*x^2+6 = 0

2*(400*x-4*x^2+3) = 0

400*x-4*x^2+3 = 0

DELTA = 400^2-(-4*3*4)

DELTA = 160048

DELTA > 0

x = (160048^(1/2)-400)/(-4*2) or x = (-160048^(1/2)-400)/(-4*2)

x = (4*10003^(1/2)-400)/(-8) or x = (-4*10003^(1/2)-400)/(-8)

2*(x-((4*10003^(1/2)-400)/(-8)))*(x-((-4*10003^(1/2)-400)/(-8))) = 0

(2*(x-((4*10003^(1/2)-400)/(-8)))*(x-((-4*10003^(1/2)-400)/(-8))))/x = 0

(2*(x-((4*10003^(1/2)-400)/(-8)))*(x-((-4*10003^(1/2)-400)/(-8))))/x = 0 // * x

2*(x-((4*10003^(1/2)-400)/(-8)))*(x-((-4*10003^(1/2)-400)/(-8))) = 0

( 2 )

2 = 0

x belongs to the empty set

( x-((-4*10003^(1/2)-400)/(-8)) )

x-((-4*10003^(1/2)-400)/(-8)) = 0 // + (-4*10003^(1/2)-400)/(-8)

x = (-4*10003^(1/2)-400)/(-8)

( x-((4*10003^(1/2)-400)/(-8)) )

x-((4*10003^(1/2)-400)/(-8)) = 0 // + (4*10003^(1/2)-400)/(-8)

x = (4*10003^(1/2)-400)/(-8)

x in { (-4*10003^(1/2)-400)/(-8), (4*10003^(1/2)-400)/(-8) }

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