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

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

3*x^-1-5/2*x^1-7/2*x^0 = 0

(3*x^0-5/2*x^2-7/2*x^1)/(x^1) = 0 // * x^2

x^1*(3*x^0-5/2*x^2-7/2*x^1) = 0

x^1

(-5/2)*x^2+(-7/2)*x+3 = 0

(-5/2)*x^2+(-7/2)*x+3 = 0

DELTA = (-7/2)^2-(3*4*(-5/2))

DELTA = 169/4

DELTA > 0

x = ((169/4)^(1/2)-(-7/2))/(2*(-5/2)) or x = (-(-7/2)-(169/4)^(1/2))/(2*(-5/2))

x = -2 or x = 3/5

x in { -2, 3/5} 

x in { -2, 3/5 }

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