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

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

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

DELTA = 89/4

DELTA > 0

x = ((89/4)^(1/2)-(5/2))/(2*(2/3)) or x = (-(5/2)-(89/4)^(1/2))/(2*(2/3))

x = 3/4*((89/4)^(1/2)-5/2) or x = -3/4*((89/4)^(1/2)+5/2)

x in { -3/4*((89/4)^(1/2)+5/2), 3/4*((89/4)^(1/2)-5/2)}

x in { -3/4*((89/4)^(1/2)+5/2), 3/4*((89/4)^(1/2)-5/2) }

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