G=x^2-6x+9/2

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Solution for G=x^2-6x+9/2 equation: 


x in (-oo:+oo)

G = x^2-(6*x)+9/2 // - x^2-(6*x)+9/2

G-x^2+6*x-(9/2) = 0

G-x^2+6*x-9/2 = 0

G-x^2+6*x-9/2 = 0

DELTA = 6^2-(-1*4*(G-9/2))

DELTA = 4*(G-9/2)+36

4*(G-9/2)+36 = 0

4*(G-9/2)+36 = 0

4*G+18 = 0

4*G+18 = 0

4*G+18 = 0 // - 18

4*G = -18 // : 4

G = -18/4

G = -9/2

DELTA = 0  <=>  t_1 = -9/2

x = -6/(-1*2) i G = -9/2

x = 3 i G = -9/2

( x = ((4*(G-9/2)+36)^(1/2)-6)/(-1*2) or x = (-(4*(G-9/2)+36)^(1/2)-6)/(-1*2) ) i G > -9/2

( x = ((4*(G-9/2)+36)^(1/2)-6)/(-2) or x = ((4*(G-9/2)+36)^(1/2)+6)/2 ) i G > -9/2

G+9/2 > 0

G+9/2 > 0 // - 9/2

G > -9/2

x in { 3, ((4*(G-9/2)+36)^(1/2)-6)/(-2), ((4*(G-9/2)+36)^(1/2)+6)/2 }

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