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D( x )
x-5 = 0
x = 0
x-5 = 0
x-5 = 0
x-5 = 0 // + 5
x = 5
x = 0
x = 0
x in (-oo:0) U (0:5) U (5:+oo)
50/x-(50/(x-5)) = -1/2 // + -1/2
50/x-(50/(x-5))-(-1/2) = 0
50/x-50*(x-5)^-1+1/2 = 0
50/x-50/(x-5)+1/2 = 0
(-50*2*x)/(2*x*(x-5))+(2*50*(x-5))/(2*x*(x-5))+(1*x*(x-5))/(2*x*(x-5)) = 0
2*50*(x-5)+1*x*(x-5)-50*2*x = 0
x^2-5*x-500 = 0
x^2-5*x-500 = 0
x^2-5*x-500 = 0
DELTA = (-5)^2-(-500*1*4)
DELTA = 2025
DELTA > 0
x = (2025^(1/2)+5)/(1*2) or x = (5-2025^(1/2))/(1*2)
x = 25 or x = -20
(x+20)*(x-25) = 0
((x+20)*(x-25))/(2*x*(x-5)) = 0
((x+20)*(x-25))/(2*x*(x-5)) = 0 // * 2*x*(x-5)
(x+20)*(x-25) = 0
( x+20 )
x+20 = 0 // - 20
x = -20
( x-25 )
x-25 = 0 // + 25
x = 25
x in { -20, 25 }
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