3/x-5/2x+5=31/6

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Solution for 3/x-5/2x+5=31/6 equation: 


D( x )

x = 0

x = 0

x = 0

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

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

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

(-5/2)*x+3/x-31/6+5 = 0

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

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

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

x^1

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

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

DELTA = (-1/6)^2-(3*4*(-5/2))

DELTA = 1081/36

DELTA > 0

x = ((1081/36)^(1/2)-(-1/6))/(2*(-5/2)) or x = (-(-1/6)-(1081/36)^(1/2))/(2*(-5/2))

x = ((1081/36)^(1/2)+1/6)/(-5) or x = (1/6-(1081/36)^(1/2))/(-5)

x in { ((1081/36)^(1/2)+1/6)/(-5), (1/6-(1081/36)^(1/2))/(-5)} 

x in { ((1081/36)^(1/2)+1/6)/(-5), (1/6-(1081/36)^(1/2))/(-5) }

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