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x in (-oo:+oo)
(x*(x+1))/2+50*x = y // - y
(x*(x+1))/2+50*x-y = 0
(x*(x+1))/2+(2*50*x)/2+(2*(-y))/2 = 0
x*(x+1)+2*50*x+2*(-y) = 0
x^2+101*x-2*y = 0
(x^2+101*x-2*y)/2 = 0
(x^2+101*x-2*y)/2 = 0 // * 2
x^2+101*x-2*y = 0
x^2+101*x-2*y = 0
DELTA = 101^2-(-2*1*4*y)
DELTA = 8*y+10201
8*y+10201 = 0
8*y+10201 = 0 // - 10201
8*y = -10201 // : 8
y = -10201/8
DELTA = 0 <=> t_3 = -10201/8
x = -101/(1*2) i y = -10201/8
x = -101/2 i y = -10201/8
( x = ((8*y+10201)^(1/2)-101)/(1*2) or x = (-(8*y+10201)^(1/2)-101)/(1*2) ) i y > -10201/8
( x = ((8*y+10201)^(1/2)-101)/2 or x = (-((8*y+10201)^(1/2)+101))/2 ) i y > -10201/8
y-(-10201/8) > 0
y+10201/8 > 0
y+10201/8 > 0 // - 10201/8
y > -10201/8
x in { -101/2, ((8*y+10201)^(1/2)-101)/2, (-((8*y+10201)^(1/2)+101))/2 }
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