3-1/x=7/5x-9/5

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Solution for 3-1/x=7/5x-9/5 equation:


D( x )

x = 0

x = 0

x = 0

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

3-(1/x) = (7/5)*x-(9/5) // - (7/5)*x-(9/5)

9/5-((7/5)*x)-(1/x)+3 = 0

(-7/5)*x-x^-1+9/5+3 = 0

24/5*x^0-7/5*x^1-1*x^-1 = 0

(24/5*x^1-7/5*x^2-1*x^0)/(x^1) = 0 // * x^2

x^1*(24/5*x^1-7/5*x^2-1*x^0) = 0

x^1

(-7/5)*x^2+(24/5)*x-1 = 0

(-7/5)*x^2+(24/5)*x-1 = 0

DELTA = (24/5)^2-(-1*4*(-7/5))

DELTA = 436/25

DELTA > 0

x = ((436/25)^(1/2)-(24/5))/(2*(-7/5)) or x = (-(24/5)-(436/25)^(1/2))/(2*(-7/5))

x = -5/14*((436/25)^(1/2)-24/5) or x = 5/14*((436/25)^(1/2)+24/5)

x in { -5/14*((436/25)^(1/2)-24/5), 5/14*((436/25)^(1/2)+24/5)}

x in { -5/14*((436/25)^(1/2)-24/5), 5/14*((436/25)^(1/2)+24/5) }

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