x/5=2/x-3

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

DELTA = 3^2-(-2*4*(1/5))

DELTA = 53/5

DELTA > 0

x = ((53/5)^(1/2)-3)/(2*(1/5)) or x = (-(53/5)^(1/2)-3)/(2*(1/5))

x = 5/2*((53/5)^(1/2)-3) or x = -5/2*((53/5)^(1/2)+3)

x in { -5/2*((53/5)^(1/2)+3), 5/2*((53/5)^(1/2)-3)}

x in { -5/2*((53/5)^(1/2)+3), 5/2*((53/5)^(1/2)-3) }

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