3/x=9/5x+2

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Solution for 3/x=9/5x+2 equation:


D( x )

x = 0

x = 0

x = 0

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

3/x = (9/5)*x+2 // - (9/5)*x+2

3/x-((9/5)*x)-2 = 0

(-9/5)*x+3/x-2 = 0

3*x^-1-9/5*x^1-2*x^0 = 0

(3*x^0-9/5*x^2-2*x^1)/(x^1) = 0 // * x^2

x^1*(3*x^0-9/5*x^2-2*x^1) = 0

x^1

(-9/5)*x^2-2*x+3 = 0

(-9/5)*x^2-2*x+3 = 0

DELTA = (-2)^2-(3*4*(-9/5))

DELTA = 128/5

DELTA > 0

x = ((128/5)^(1/2)+2)/(2*(-9/5)) or x = (2-(128/5)^(1/2))/(2*(-9/5))

x = -5/18*((128/5)^(1/2)+2) or x = -5/18*(2-(128/5)^(1/2))

x in { -5/18*((128/5)^(1/2)+2), -5/18*(2-(128/5)^(1/2))}

x in { -5/18*((128/5)^(1/2)+2), -5/18*(2-(128/5)^(1/2)) }

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