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D( x )
x^2-200 = 0
x^2-200 = 0
x^2-200 = 0
1*x^2 = 200 // : 1
x^2 = 200
x^2 = 200 // ^ 1/2
abs(x) = 10*2^(1/2)
x = 10*2^(1/2) or x = -(10*2^(1/2))
x in (-oo:-(10*2^(1/2))) U (-(10*2^(1/2)):10*2^(1/2)) U (10*2^(1/2):+oo)
6 = (120*x)/(x^2-200) // - (120*x)/(x^2-200)
6-((120*x)/(x^2-200)) = 0
6-120*x*(x^2-200)^-1 = 0
(-120*x)/(x^2-200)+6 = 0
(-120*x)/(x^2-200)+(6*(x^2-200))/(x^2-200) = 0
6*(x^2-200)-120*x = 0
6*x^2-120*x-1200 = 0
6*x^2-120*x-1200 = 0
6*(x^2-20*x-200) = 0
x^2-20*x-200 = 0
DELTA = (-20)^2-(-200*1*4)
DELTA = 1200
DELTA > 0
x = (1200^(1/2)+20)/(1*2) or x = (20-1200^(1/2))/(1*2)
x = (20*3^(1/2)+20)/2 or x = (20-20*3^(1/2))/2
6*(x-((20-20*3^(1/2))/2))*(x-((20*3^(1/2)+20)/2)) = 0
(6*(x-((20-20*3^(1/2))/2))*(x-((20*3^(1/2)+20)/2)))/(x^2-200) = 0
(6*(x-((20-20*3^(1/2))/2))*(x-((20*3^(1/2)+20)/2)))/(x^2-200) = 0 // * x^2-200
6*(x-((20-20*3^(1/2))/2))*(x-((20*3^(1/2)+20)/2)) = 0
( 6 )
6 = 0
x belongs to the empty set
( x-((20*3^(1/2)+20)/2) )
x-((20*3^(1/2)+20)/2) = 0 // + (20*3^(1/2)+20)/2
x = (20*3^(1/2)+20)/2
( x-((20-20*3^(1/2))/2) )
x-((20-20*3^(1/2))/2) = 0 // + (20-20*3^(1/2))/2
x = (20-20*3^(1/2))/2
x in { (20*3^(1/2)+20)/2, (20-20*3^(1/2))/2 }
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