(4/x)+5=(5/2x)+(31/6)

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Solution for (4/x)+5=(5/2x)+(31/6) equation: 


D( x )

x = 0

x = 0

x = 0

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

4/x+5 = (5/2)*x+31/6 // - (5/2)*x+31/6

4/x-((5/2)*x)-(31/6)+5 = 0

(-5/2)*x+4/x-31/6+5 = 0

4*x^-1-5/2*x^1-1/6*x^0 = 0

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

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

x^1

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

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

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

DELTA = 1441/36

DELTA > 0

x = ((1441/36)^(1/2)-(-1/6))/(2*(-5/2)) or x = (-(-1/6)-(1441/36)^(1/2))/(2*(-5/2))

x = ((1441/36)^(1/2)+1/6)/(-5) or x = (1/6-(1441/36)^(1/2))/(-5)

x in { ((1441/36)^(1/2)+1/6)/(-5), (1/6-(1441/36)^(1/2))/(-5)} 

x in { ((1441/36)^(1/2)+1/6)/(-5), (1/6-(1441/36)^(1/2))/(-5) }

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