Y=x^2-4/3x-6

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Solution for Y=x^2-4/3x-6 equation: 


x in (-oo:+oo)

Y = x^2-((4/3)*x)-6 // - x^2-((4/3)*x)-6

Y-x^2+(4/3)*x+6 = 0

Y-x^2+4/3*x+6 = 0

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

DELTA = 4*(Y+6)+16/9

4*(Y+6)+16/9 = 0

(4*9*(Y+6))/9+16/9 = 0

4*9*(Y+6)+16 = 0

36*Y+232 = 0

(36*Y+232)/9 = 0

(36*Y+232)/9 = 0 // * 9

36*Y+232 = 0

36*Y+232 = 0 // - 232

36*Y = -232 // : 36

Y = -232/36

Y = -58/9

DELTA = 0  <=>  t_1 = -58/9

x = -4/3/(-1*2) i Y = -58/9

x = 2/3 i Y = -58/9

( x = ((4*(Y+6)+16/9)^(1/2)-4/3)/(-1*2) or x = (-(4*(Y+6)+16/9)^(1/2)-4/3)/(-1*2) ) i Y > -58/9

( x = ((4*(Y+6)+16/9)^(1/2)-4/3)/(-2) or x = ((4*(Y+6)+16/9)^(1/2)+4/3)/2 ) i Y > -58/9

Y+58/9 > 0

Y+58/9 > 0 // - 58/9

Y > -58/9

x in { 2/3, ((4*(Y+6)+16/9)^(1/2)-4/3)/(-2), ((4*(Y+6)+16/9)^(1/2)+4/3)/2 }

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