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

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

x in (-oo:+oo)

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

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

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

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

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

DELTA = 2/3*(Y+3)+1

2/3*(Y+3)+1 = 0

2/3*(Y+3)+1 = 0

2/3*Y+3 = 0

2/3*Y+3 = 0

2/3*Y+3 = 0 // - 3

2/3*Y = -3 // : 2/3

Y = -3/2/3

Y = -9/2

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

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

x = 3 i Y = -9/2

( x = ((2/3*(Y+3)+1)^(1/2)-1)/(-1/6*2) or x = (-(2/3*(Y+3)+1)^(1/2)-1)/(-1/6*2) ) i Y > -9/2

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

Y+9/2 > 0

Y+9/2 > 0 // - 9/2

Y > -9/2

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