x^2+y^2-2/3x-2/3y-14/9=0

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Solution for x^2+y^2-2/3x-2/3y-14/9=0 equation:


x in (-oo:+oo)

t_1 = y^2-2/3*y-14/9

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

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

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

DELTA = 4/9-4*t_1

4/9-4*t_1 = 0

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

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

t_1 = -4/9/(-4)

t_1 = 1/9

DELTA = 0 <=> t_2 = 1/9

x = 2/3/(1*2) i t_1 = 1/9

x = 1/3 i t_1 = 1/9

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

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

t_1-1/9 > 0

t_1-1/9 > 0 // + 1/9

t_1 > 1/9

x in { 1/3, ((4/9-4*(y^2-2/3*y-14/9))^(1/2)+2/3)/2, (2/3-(4/9-4*(y^2-2/3*y-14/9))^(1/2))/2 }

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