y=1/2x^2-6x

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Solution for y=1/2x^2-6x equation:


x in (-oo:+oo)

y = (1/2)*x^2-(6*x) // - (1/2)*x^2-(6*x)

6*x-((1/2)*x^2)+y = 0

(-1/2)*x^2+6*x+y = 0

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

DELTA = 6^2-(-1/2*4*y)

DELTA = 2*y+36

2*y+36 = 0

2*y+36 = 0 // - 36

2*y = -36 // : 2

y = -36/2

y = -18

DELTA = 0 <=> t_1 = -18

x = -6/(-1/2*2) i y = -18

x = 6 i y = -18

( x = ((2*y+36)^(1/2)-6)/(-1/2*2) or x = (-(2*y+36)^(1/2)-6)/(-1/2*2) ) i y > -18

( x = 6-(2*y+36)^(1/2) or x = (2*y+36)^(1/2)+6 ) i y > -18

y+18 > 0

y+18 > 0 // - 18

y > -18

x in { 6, 6-(2*y+36)^(1/2), (2*y+36)^(1/2)+6 }

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