(5/x)-(3/2x)=(x/2)

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Solution for (5/x)-(3/2x)=(x/2) equation: 


D( x )

x = 0

x = 0

x = 0

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

5/x-((3/2)*x) = x/2 // - x/2

5/x-((3/2)*x)-(x/2) = 0

(-3/2)*x-(x/2)+5/x = 0

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

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

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

x^1

5-2*x^2 = 0

5-2*x^2 = 0

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

DELTA = 40

DELTA > 0

x = (40^(1/2)+0)/(-2*2) or x = (0-40^(1/2))/(-2*2)

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

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

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

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