y=1/2x^2-6x-3

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Solution for y=1/2x^2-6x-3 equation:


x in (-oo:+oo)

y = (1/2)*x^2-(6*x)-3 // - (1/2)*x^2-(6*x)-3

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

(-1/2)*x^2+6*x+y+3 = 0

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

DELTA = 6^2-(-1/2*4*(y+3))

DELTA = 2*(y+3)+36

2*(y+3)+36 = 0

2*(y+3)+36 = 0

2*y+42 = 0

2*y+42 = 0

2*y+42 = 0 // - 42

2*y = -42 // : 2

y = -42/2

y = -21

DELTA = 0 <=> t_1 = -21

x = -6/(-1/2*2) i y = -21

x = 6 i y = -21

( x = ((2*(y+3)+36)^(1/2)-6)/(-1/2*2) or x = (-(2*(y+3)+36)^(1/2)-6)/(-1/2*2) ) i y > -21

( x = 6-(2*(y+3)+36)^(1/2) or x = (2*(y+3)+36)^(1/2)+6 ) i y > -21

y+21 > 0

y+21 > 0 // - 21

y > -21

x in { 6, 6-(2*(y+3)+36)^(1/2), (2*(y+3)+36)^(1/2)+6 }

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