x=5/(400-20x)

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Solution for x=5/(400-20x) equation:


D( x )

400-(20*x) = 0

400-(20*x) = 0

400-(20*x) = 0

400-20*x = 0

400-20*x = 0 // - 400

-20*x = -400 // : -20

x = -400/(-20)

x = 20

x in (-oo:20) U (20:+oo)

x = 5/(400-(20*x)) // - 5/(400-(20*x))

x-(5/(400-(20*x))) = 0

x-5*(400-20*x)^-1 = 0

x-5/(400-20*x) = 0

(x*(400-20*x))/(400-20*x)-5/(400-20*x) = 0

x*(400-20*x)-5 = 0

400*x-20*x^2-5 = 0

400*x-20*x^2-5 = 0

5*(80*x-4*x^2-1) = 0

80*x-4*x^2-1 = 0

DELTA = 80^2-(-4*(-1)*4)

DELTA = 6384

DELTA > 0

x = (6384^(1/2)-80)/(-4*2) or x = (-6384^(1/2)-80)/(-4*2)

x = (4*399^(1/2)-80)/(-8) or x = (-4*399^(1/2)-80)/(-8)

5*(x-((4*399^(1/2)-80)/(-8)))*(x-((-4*399^(1/2)-80)/(-8))) = 0

(5*(x-((4*399^(1/2)-80)/(-8)))*(x-((-4*399^(1/2)-80)/(-8))))/(400-20*x) = 0

(5*(x-((4*399^(1/2)-80)/(-8)))*(x-((-4*399^(1/2)-80)/(-8))))/(400-20*x) = 0 // * 400-20*x

5*(x-((4*399^(1/2)-80)/(-8)))*(x-((-4*399^(1/2)-80)/(-8))) = 0

( 5 )

5 = 0

x belongs to the empty set

( x-((-4*399^(1/2)-80)/(-8)) )

x-((-4*399^(1/2)-80)/(-8)) = 0 // + (-4*399^(1/2)-80)/(-8)

x = (-4*399^(1/2)-80)/(-8)

( x-((4*399^(1/2)-80)/(-8)) )

x-((4*399^(1/2)-80)/(-8)) = 0 // + (4*399^(1/2)-80)/(-8)

x = (4*399^(1/2)-80)/(-8)

x in { (-4*399^(1/2)-80)/(-8), (4*399^(1/2)-80)/(-8) }

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