5/6x-18-2/3=4/x-3

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Solution for 5/6x-18-2/3=4/x-3 equation: 


D( x )

x = 0

x = 0

x = 0

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

(5/6)*x-(2/3)-18 = 4/x-3 // - 4/x-3

(5/6)*x-(4/x)-(2/3)-18+3 = 0

(5/6)*x-4*x^-1-2/3-18+3 = 0

5/6*x^1-4*x^-1-47/3*x^0 = 0

(5/6*x^2-47/3*x^1-4*x^0)/(x^1) = 0 // * x^2

x^1*(5/6*x^2-47/3*x^1-4*x^0) = 0

x^1

(5/6)*x^2+(-47/3)*x-4 = 0

(5/6)*x^2+(-47/3)*x-4 = 0

DELTA = (-47/3)^2-(-4*4*(5/6))

DELTA = 2329/9

DELTA > 0

x = ((2329/9)^(1/2)-(-47/3))/(2*(5/6)) or x = (-(-47/3)-(2329/9)^(1/2))/(2*(5/6))

x = 3/5*((2329/9)^(1/2)+47/3) or x = 3/5*(47/3-(2329/9)^(1/2))

x in { 3/5*(47/3-(2329/9)^(1/2)), 3/5*((2329/9)^(1/2)+47/3)} 

x in { 3/5*(47/3-(2329/9)^(1/2)), 3/5*((2329/9)^(1/2)+47/3) }

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