(5/x)+(2/3)=(1/6x)

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Solution for (5/x)+(2/3)=(1/6x) equation:


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

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

DELTA = 34/9

DELTA > 0

x = ((34/9)^(1/2)-(2/3))/(2*(-1/6)) or x = (-(2/3)-(34/9)^(1/2))/(2*(-1/6))

x = -3*((34/9)^(1/2)-2/3) or x = 3*((34/9)^(1/2)+2/3)

x in { -3*((34/9)^(1/2)-2/3), 3*((34/9)^(1/2)+2/3)}

x in { -3*((34/9)^(1/2)-2/3), 3*((34/9)^(1/2)+2/3) }

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