5x/x^2-10x

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Solution for 5x/x^2-10x equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

(5*x)/(x^2)-(10*x) = 0

(5*x)/(x^2)-10*x = 0

5*x^-1-10*x^1 = 0

(5*x^0-10*x^2)/(x^1) = 0 // * x^2

x^1*(5*x^0-10*x^2) = 0

x^1

5-10*x^2 = 0

5-10*x^2 = 0

DELTA = 0^2-(-10*4*5)

DELTA = 200

DELTA > 0

x = (200^(1/2)+0)/(-10*2) or x = (0-200^(1/2))/(-10*2)

x = (-2^(1/2))/2 or x = (2^(1/2))/2

x in { (-2^(1/2))/2, (2^(1/2))/2} 

x in { (-2^(1/2))/2, (2^(1/2))/2 }

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