5/x=x/9

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Solution for 5/x=x/9 equation: 


D( x )

x = 0

x = 0

x = 0

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

5/x = x/9 // - x/9

5/x-(x/9) = 0

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

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

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

x^1

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

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

DELTA = 0^2-(4*5*(-1/9))

DELTA = 20/9

DELTA > 0

x = ((20/9)^(1/2)+0)/(2*(-1/9)) or x = (0-(20/9)^(1/2))/(2*(-1/9))

x = -9/2*(20/9)^(1/2) or x = 9/2*(20/9)^(1/2)

x in { -9/2*(20/9)^(1/2), 9/2*(20/9)^(1/2)} 

x in { -9/2*(20/9)^(1/2), 9/2*(20/9)^(1/2) }

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