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

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

5*x^-1-2/3*x^1-1/6*x^0 = 0

(5*x^0-2/3*x^2-1/6*x^1)/(x^1) = 0 // * x^2

x^1*(5*x^0-2/3*x^2-1/6*x^1) = 0

x^1

(-2/3)*x^2+(-1/6)*x+5 = 0

(-2/3)*x^2+(-1/6)*x+5 = 0

DELTA = (-1/6)^2-(4*5*(-2/3))

DELTA = 481/36

DELTA > 0

x = ((481/36)^(1/2)-(-1/6))/(2*(-2/3)) or x = (-(-1/6)-(481/36)^(1/2))/(2*(-2/3))

x = -3/4*((481/36)^(1/2)+1/6) or x = -3/4*(1/6-(481/36)^(1/2))

x in { -3/4*((481/36)^(1/2)+1/6), -3/4*(1/6-(481/36)^(1/2))} 

x in { -3/4*((481/36)^(1/2)+1/6), -3/4*(1/6-(481/36)^(1/2)) }

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