6-5/x=1/2x

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Solution for 6-5/x=1/2x equation: 


D( x )

x = 0

x = 0

x = 0

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

6-(5/x) = (1/2)*x // - (1/2)*x

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

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

6*x^0-1/2*x^1-5*x^-1 = 0

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

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

x^1

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

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

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

DELTA = 26

DELTA > 0

x = (26^(1/2)-6)/(2*(-1/2)) or x = (-26^(1/2)-6)/(2*(-1/2))

x = 6-26^(1/2) or x = 26^(1/2)+6

x in { 6-26^(1/2), 26^(1/2)+6} 

x in { 6-26^(1/2), 26^(1/2)+6 }

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