(100/x)-5x=(-25/x)

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Solution for (100/x)-5x=(-25/x) equation: 


D( x )

x = 0

x = 0

x = 0

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

100/x-(5*x) = -25/x // + -25/x

100/x-(5*x)-(-25/x) = 0

100/x-5*x+25*x^-1 = 0

125*x^-1-5*x^1 = 0

(125*x^0-5*x^2)/(x^1) = 0 // * x^2

x^1*(125*x^0-5*x^2) = 0

x^1

125-5*x^2 = 0

125-5*x^2 = 0

DELTA = 0^2-(-5*4*125)

DELTA = 2500

DELTA > 0

x = (2500^(1/2)+0)/(-5*2) or x = (0-2500^(1/2))/(-5*2)

x = -5 or x = 5

x in { -5, 5} 

x in { -5, 5 }

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