(5/x)+3=(9/2x)+(19/6)

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Solution for (5/x)+3=(9/2x)+(19/6) equation: 


D( x )

x = 0

x = 0

x = 0

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

5/x+3 = (9/2)*x+19/6 // - (9/2)*x+19/6

5/x-((9/2)*x)-(19/6)+3 = 0

(-9/2)*x+5/x-19/6+3 = 0

5*x^-1-9/2*x^1-1/6*x^0 = 0

(5*x^0-9/2*x^2-1/6*x^1)/(x^1) = 0 // * x^2

x^1*(5*x^0-9/2*x^2-1/6*x^1) = 0

x^1

(-9/2)*x^2+(-1/6)*x+5 = 0

(-9/2)*x^2+(-1/6)*x+5 = 0

DELTA = (-1/6)^2-(4*5*(-9/2))

DELTA = 3241/36

DELTA > 0

x = ((3241/36)^(1/2)-(-1/6))/(2*(-9/2)) or x = (-(-1/6)-(3241/36)^(1/2))/(2*(-9/2))

x = ((3241/36)^(1/2)+1/6)/(-9) or x = (1/6-(3241/36)^(1/2))/(-9)

x in { ((3241/36)^(1/2)+1/6)/(-9), (1/6-(3241/36)^(1/2))/(-9)} 

x in { ((3241/36)^(1/2)+1/6)/(-9), (1/6-(3241/36)^(1/2))/(-9) }

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