x^2+1/3x+y^2-10/3y=127/9

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Solution for x^2+1/3x+y^2-10/3y=127/9 equation: 


x in (-oo:+oo)

t_1 = y^2-10/3*y-127/9

t_1+x^2+1/3*x = 0

t_1+x^2+1/3*x = 0

DELTA = (1/3)^2-(1*4*t_1)

DELTA = 1/9-4*t_1

1/9-4*t_1 = 0

1/9-4*t_1 = 0 // - 1/9

-4*t_1 = -1/9 // : -4

t_1 = -1/9/(-4)

t_1 = 1/36

DELTA = 0  <=>  t_2 = 1/36

x = -1/3/(1*2) i t_1 = 1/36

x = -1/6 i t_1 = 1/36

( x = ((1/9-4*t_1)^(1/2)-1/3)/(1*2) or x = (-(1/9-4*t_1)^(1/2)-1/3)/(1*2) ) i t_1 > 1/36

( x = ((1/9-4*t_1)^(1/2)-1/3)/2 or x = (-((1/9-4*t_1)^(1/2)+1/3))/2 ) i t_1 > 1/36

t_1-1/36 > 0

t_1-1/36 > 0 // + 1/36

t_1 > 1/36

x in { -1/6, ((1/9-4*(y^2-10/3*y-127/9))^(1/2)-1/3)/2, (-((1/9-4*(y^2-10/3*y-127/9))^(1/2)+1/3))/2 }

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