x/6+3/x=2x/3+25/2

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Solution for x/6+3/x=2x/3+25/2 equation: 


D( x )

x = 0

x = 0

x = 0

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

x/6+3/x = (2*x)/3+25/2 // - (2*x)/3+25/2

x/6-((2*x)/3)+3/x-(25/2) = 0

x/6+(-2/3)*x+3/x-25/2 = 0

3*x^-1-1/2*x^1-25/2*x^0 = 0

(3*x^0-1/2*x^2-25/2*x^1)/(x^1) = 0 // * x^2

x^1*(3*x^0-1/2*x^2-25/2*x^1) = 0

x^1

(-1/2)*x^2+(-25/2)*x+3 = 0

(-1/2)*x^2+(-25/2)*x+3 = 0

DELTA = (-25/2)^2-(3*4*(-1/2))

DELTA = 649/4

DELTA > 0

x = ((649/4)^(1/2)-(-25/2))/(2*(-1/2)) or x = (-(-25/2)-(649/4)^(1/2))/(2*(-1/2))

x = -((649/4)^(1/2)+25/2) or x = (649/4)^(1/2)-25/2

x in { -((649/4)^(1/2)+25/2), (649/4)^(1/2)-25/2} 

x in { -((649/4)^(1/2)+25/2), (649/4)^(1/2)-25/2 }

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