8/x-5=2x

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Solution for 8/x-5=2x equation: 


D( x )

x = 0

x = 0

x = 0

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

8/x-5 = 2*x // - 2*x

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

8/x-2*x-5 = 0

8*x^-1-2*x^1-5*x^0 = 0

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

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

x^1

8-2*x^2-5*x = 0

8-2*x^2-5*x = 0

DELTA = (-5)^2-(-2*4*8)

DELTA = 89

DELTA > 0

x = (89^(1/2)+5)/(-2*2) or x = (5-89^(1/2))/(-2*2)

x = (89^(1/2)+5)/(-4) or x = (5-89^(1/2))/(-4)

x in { (89^(1/2)+5)/(-4), (5-89^(1/2))/(-4)} 

x in { (89^(1/2)+5)/(-4), (5-89^(1/2))/(-4) }

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