3/x-x=x/10-5/2

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Solution for 3/x-x=x/10-5/2 equation: 


D( x )

x = 0

x = 0

x = 0

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

3/x-x = x/10-(5/2) // - x/10-(5/2)

3/x-x-(x/10)+5/2 = 0

3*x^-1-11/10*x^1+5/2*x^0 = 0

(5/2*x^1-11/10*x^2+3*x^0)/(x^1) = 0 // * x^2

x^1*(5/2*x^1-11/10*x^2+3*x^0) = 0

x^1

(-11/10)*x^2+(5/2)*x+3 = 0

(-11/10)*x^2+(5/2)*x+3 = 0

DELTA = (5/2)^2-(3*4*(-11/10))

DELTA = 389/20

DELTA > 0

x = ((389/20)^(1/2)-(5/2))/(2*(-11/10)) or x = (-(5/2)-(389/20)^(1/2))/(2*(-11/10))

x = -5/11*((389/20)^(1/2)-5/2) or x = 5/11*((389/20)^(1/2)+5/2)

x in { -5/11*((389/20)^(1/2)-5/2), 5/11*((389/20)^(1/2)+5/2)} 

x in { -5/11*((389/20)^(1/2)-5/2), 5/11*((389/20)^(1/2)+5/2) }

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