5/x=x+13/6

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Solution for 5/x=x+13/6 equation: 


D( x )

x = 0

x = 0

x = 0

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

5/x = x+13/6 // - x+13/6

5/x-x-(13/6) = 0

5/x-x-13/6 = 0

5*x^-1-1*x^1-13/6*x^0 = 0

(5*x^0-1*x^2-13/6*x^1)/(x^1) = 0 // * x^2

x^1*(5*x^0-1*x^2-13/6*x^1) = 0

x^1

(-13/6)*x-x^2+5 = 0

(-13/6)*x-x^2+5 = 0

DELTA = (-13/6)^2-(-1*4*5)

DELTA = 889/36

DELTA > 0

x = ((889/36)^(1/2)-(-13/6))/(-1*2) or x = (-(-13/6)-(889/36)^(1/2))/(-1*2)

x = ((889/36)^(1/2)+13/6)/(-2) or x = (13/6-(889/36)^(1/2))/(-2)

x in { ((889/36)^(1/2)+13/6)/(-2), (13/6-(889/36)^(1/2))/(-2)} 

x in { ((889/36)^(1/2)+13/6)/(-2), (13/6-(889/36)^(1/2))/(-2) }

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