2x-3y^2+8/7x^2+8y=9

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Solution for 2x-3y^2+8/7x^2+8y=9 equation: 


x in (-oo:+oo)

t_1 = 8*y-3*y^2-9

t_1+8/7*x^2+2*x = 0

t_1+8/7*x^2+2*x = 0

DELTA = 2^2-(8/7*4*t_1)

DELTA = 4-32/7*t_1

4-32/7*t_1 = 0

4-32/7*t_1 = 0 // - 4

-32/7*t_1 = -4 // : -32/7

t_1 = -4/(-32/7)

t_1 = 7/8

DELTA = 0  <=>  t_2 = 7/8

x = -2/(8/7*2) i t_1 = 7/8

x = -7/8 i t_1 = 7/8

( x = ((4-32/7*t_1)^(1/2)-2)/(8/7*2) or x = (-(4-32/7*t_1)^(1/2)-2)/(8/7*2) ) i t_1 > 7/8

( x = 7/16*((4-32/7*t_1)^(1/2)-2) or x = -7/16*((4-32/7*t_1)^(1/2)+2) ) i t_1 > 7/8

t_1-7/8 > 0

t_1-7/8 > 0 // + 7/8

t_1 > 7/8

x in { -7/8, 7/16*((4-32/7*(8*y-3*y^2-9))^(1/2)-2), -7/16*((4-32/7*(8*y-3*y^2-9))^(1/2)+2) }

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