5/x=x/8

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Solution for 5/x=x/8 equation: 


D( x )

x = 0

x = 0

x = 0

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

5/x = x/8 // - x/8

5/x-(x/8) = 0

5*x^-1-1/8*x^1 = 0

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

x^1*(5*x^0-1/8*x^2) = 0

x^1

(-1/8)*x^2+5 = 0

(-1/8)*x^2+5 = 0

DELTA = 0^2-(4*5*(-1/8))

DELTA = 5/2

DELTA > 0

x = ((5/2)^(1/2)+0)/(2*(-1/8)) or x = (0-(5/2)^(1/2))/(2*(-1/8))

x = -4*(5/2)^(1/2) or x = 4*(5/2)^(1/2)

x in { -4*(5/2)^(1/2), 4*(5/2)^(1/2)} 

x in { -4*(5/2)^(1/2), 4*(5/2)^(1/2) }

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