x-(x-3)/x+6

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Solution for x-(x-3)/x+6 equation: 


D( x )

x = 0

x = 0

x = 0

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

x-((x-3)/x)+6 = 0

(-1*(x-3))/x+x+6 = 0

(-1*(x-3))/x+(x^2)/x+(6*x)/x = 0

x^2-1*(x-3)+6*x = 0

x^2-x+6*x+3 = 0

x^2+5*x+3 = 0

x^2+5*x+3 = 0

x^2+5*x+3 = 0

DELTA = 5^2-(1*3*4)

DELTA = 13

DELTA > 0

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

x = (13^(1/2)-5)/2 or x = (-(13^(1/2)+5))/2

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

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

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

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

( x+(13^(1/2)+5)/2 )

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

x = -((13^(1/2)+5)/2)

( x-((13^(1/2)-5)/2) )

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

x = (13^(1/2)-5)/2

x in { -((13^(1/2)+5)/2), (13^(1/2)-5)/2 }

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