3x=4/x-13/2

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Solution for 3x=4/x-13/2 equation: 


D( x )

x = 0

x = 0

x = 0

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

3*x = 4/x-(13/2) // - 4/x-(13/2)

3*x-(4/x)+13/2 = 0

3*x-4*x^-1+13/2 = 0

3*x^1-4*x^-1+13/2*x^0 = 0

(3*x^2+13/2*x^1-4*x^0)/(x^1) = 0 // * x^2

x^1*(3*x^2+13/2*x^1-4*x^0) = 0

x^1

3*x^2+(13/2)*x-4 = 0

3*x^2+(13/2)*x-4 = 0

DELTA = (13/2)^2-(-4*3*4)

DELTA = 361/4

DELTA > 0

x = ((361/4)^(1/2)-(13/2))/(2*3) or x = (-(13/2)-(361/4)^(1/2))/(2*3)

x = 1/2 or x = -8/3

x in { -8/3, 1/2} 

x in { -8/3, 1/2 }

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