5/6x+1/2=8/x+4/3

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Solution for 5/6x+1/2=8/x+4/3 equation: 


D( x )

x = 0

x = 0

x = 0

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

(5/6)*x+1/2 = 8/x+4/3 // - 8/x+4/3

(5/6)*x-(8/x)+1/2-(4/3) = 0

(5/6)*x-8*x^-1+1/2-4/3 = 0

5/6*x^1-8*x^-1-5/6*x^0 = 0

(5/6*x^2-5/6*x^1-8*x^0)/(x^1) = 0 // * x^2

x^1*(5/6*x^2-5/6*x^1-8*x^0) = 0

x^1

(5/6)*x^2+(-5/6)*x-8 = 0

(5/6)*x^2+(-5/6)*x-8 = 0

DELTA = (-5/6)^2-(-8*4*(5/6))

DELTA = 985/36

DELTA > 0

x = ((985/36)^(1/2)-(-5/6))/(2*(5/6)) or x = (-(-5/6)-(985/36)^(1/2))/(2*(5/6))

x = 3/5*((985/36)^(1/2)+5/6) or x = 3/5*(5/6-(985/36)^(1/2))

x in { 3/5*(5/6-(985/36)^(1/2)), 3/5*((985/36)^(1/2)+5/6)} 

x in { 3/5*(5/6-(985/36)^(1/2)), 3/5*((985/36)^(1/2)+5/6) }

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