5x=10x-1/x

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Solution for 5x=10x-1/x equation: 


D( x )

x = 0

x = 0

x = 0

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

5*x = 10*x-(1/x) // - 10*x-(1/x)

5*x-(10*x)+1/x = 0

5*x-10*x+1/x = 0

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

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

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

x^1

1-5*x^2 = 0

1-5*x^2 = 0

DELTA = 0^2-(-5*1*4)

DELTA = 20

DELTA > 0

x = (20^(1/2)+0)/(-5*2) or x = (0-20^(1/2))/(-5*2)

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

x in { (-5^(1/2))/5, (1*5^(1/2))/5} 

x in { (-5^(1/2))/5, (1*5^(1/2))/5 }

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