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x in (-oo:+oo)
x*((200*x-5000)/200) = 0.25 // - 0.25
x*((200*x-5000)/200)-0.25 = 0
(x*(200*x-5000))/200-0.25 = 0
(x*(200*x-5000))/200+(-0.25*200)/200 = 0
x*(200*x-5000)-0.25*200 = 0
200*x^2-5000*x-50 = 0
200*x^2-5000*x-50 = 0
50*(4*x^2-100*x-1) = 0
4*x^2-100*x-1 = 0
DELTA = (-100)^2-(-1*4*4)
DELTA = 10016
DELTA > 0
x = (10016^(1/2)+100)/(2*4) or x = (100-10016^(1/2))/(2*4)
x = (4*626^(1/2)+100)/8 or x = (100-4*626^(1/2))/8
50*(x-((100-4*626^(1/2))/8))*(x-((4*626^(1/2)+100)/8)) = 0
(50*(x-((100-4*626^(1/2))/8))*(x-((4*626^(1/2)+100)/8)))/200 = 0
(50*(x-((100-4*626^(1/2))/8))*(x-((4*626^(1/2)+100)/8)))/200 = 0 // * 200
50*(x-((100-4*626^(1/2))/8))*(x-((4*626^(1/2)+100)/8)) = 0
( 50 )
50 = 0
x belongs to the empty set
( x-((100-4*626^(1/2))/8) )
x-((100-4*626^(1/2))/8) = 0 // + (100-4*626^(1/2))/8
x = (100-4*626^(1/2))/8
( x-((4*626^(1/2)+100)/8) )
x-((4*626^(1/2)+100)/8) = 0 // + (4*626^(1/2)+100)/8
x = (4*626^(1/2)+100)/8
x in { (100-4*626^(1/2))/8, (4*626^(1/2)+100)/8 }
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