3/2x=8/x+4

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Solution for 3/2x=8/x+4 equation: 


D( x )

x = 0

x = 0

x = 0

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

(3/2)*x = 8/x+4 // - 8/x+4

(3/2)*x-(8/x)-4 = 0

(3/2)*x-8*x^-1-4 = 0

3/2*x^1-8*x^-1-4*x^0 = 0

(3/2*x^2-4*x^1-8*x^0)/(x^1) = 0 // * x^2

x^1*(3/2*x^2-4*x^1-8*x^0) = 0

x^1

(3/2)*x^2-4*x-8 = 0

(3/2)*x^2-4*x-8 = 0

DELTA = (-4)^2-(-8*4*(3/2))

DELTA = 64

DELTA > 0

x = (64^(1/2)+4)/(2*(3/2)) or x = (4-64^(1/2))/(2*(3/2))

x = 4 or x = -4/3

x in { -4/3, 4} 

x in { -4/3, 4 }

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