5x=10-1/x

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


D( x )

x = 0

x = 0

x = 0

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

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

5*x+1/x-10 = 0

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

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

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

x^1

5*x^2-10*x+1 = 0

5*x^2-10*x+1 = 0

DELTA = (-10)^2-(1*4*5)

DELTA = 80

DELTA > 0

x = (80^(1/2)+10)/(2*5) or x = (10-80^(1/2))/(2*5)

x = (4*5^(1/2)+10)/10 or x = (10-4*5^(1/2))/10

x in { (10-4*5^(1/2))/10, (4*5^(1/2)+10)/10} 

x in { (10-4*5^(1/2))/10, (4*5^(1/2)+10)/10 }

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