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x in (-oo:+oo)
y = (1/2)*(x-5)^2-3 // - (1/2)*(x-5)^2-3
y-((1/2)*(x-5)^2)+3 = 0
(-1/2)*(x-5)^2+y+3 = 0
y-1/2*(x-5)^2+3 = 0
y-1/2*(x-5)^2+3 = 0
5*x-1/2*x^2+y-25/2+3 = 0
5*x-1/2*x^2+y-19/2 = 0
5*x-1/2*x^2+y-19/2 = 0
5*x-1/2*x^2+y-19/2 = 0
DELTA = 5^2-(-1/2*4*(y-19/2))
DELTA = 2*(y-19/2)+25
2*(y-19/2)+25 = 0
2*(y-19/2)+25 = 0
2*y+6 = 0
2*y+6 = 0
2*y+6 = 0 // - 6
2*y = -6 // : 2
y = -6/2
y = -3
DELTA = 0 <=> t_3 = -3
x = -5/(-1/2*2) i y = -3
x = 5 i y = -3
( x = ((2*(y-19/2)+25)^(1/2)-5)/(-1/2*2) or x = (-(2*(y-19/2)+25)^(1/2)-5)/(-1/2*2) ) i y > -3
( x = 5-(2*(y-19/2)+25)^(1/2) or x = (2*(y-19/2)+25)^(1/2)+5 ) i y > -3
y+3 > 0
y+3 > 0 // - 3
y > -3
x in { 5, 5-(2*(y-19/2)+25)^(1/2), (2*(y-19/2)+25)^(1/2)+5 }
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