y=x^2/2-3x+3

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Solution for y=x^2/2-3x+3 equation:


x in (-oo:+oo)

y = (x^2)/2-(3*x)+3 // - (x^2)/2-(3*x)+3

3*x-((x^2)/2)+y-3 = 0

3*x-1/2*x^2+y-3 = 0

DELTA = 3^2-(-1/2*4*(y-3))

DELTA = 2*(y-3)+9

2*(y-3)+9 = 0

2*(y-3)+9 = 0

2*y+3 = 0

2*y+3 = 0

2*y+3 = 0 // - 3

2*y = -3 // : 2

y = -3/2

DELTA = 0 <=> t_1 = -3/2

x = -3/(-1/2*2) i y = -3/2

x = 3 i y = -3/2

( x = ((2*(y-3)+9)^(1/2)-3)/(-1/2*2) or x = (-(2*(y-3)+9)^(1/2)-3)/(-1/2*2) ) i y > -3/2

( x = 3-(2*(y-3)+9)^(1/2) or x = (2*(y-3)+9)^(1/2)+3 ) i y > -3/2

y-(-3/2) > 0

y+3/2 > 0

y+3/2 > 0 // - 3/2

y > -3/2

x in { 3, 3-(2*(y-3)+9)^(1/2), (2*(y-3)+9)^(1/2)+3 }

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