What are all the solutions? 4x^2+9y^2=72 x - y 2 = -1

Given:
4x^2+9y^2=72 ......................................(1)
Assuming the second equation is
x-y^2=-1................................................(2)

Rewrite (2) as y^2=x+1 ........................(2a)
and substitute in (1)
4x^2+9(x+1)=72 =>
4x^2+9x-64=0.......................................(3)

Solve (3) by quadratic formula:
x=(-9 ± √ (1105) )/8
={-5.280, 3.030}  [ to three places after decimal ]

Substitute in (2a) to solve for y.
y= ± sqrt(-4.280) or  ± sqrt(4.030)  or
y= ± 2.0689i  and ± 2.0075
ALL four solutions are: {(-5.2802,2.0689i),(-5.2802,-2.0689i),(3.0302,2.0075),(3.0302,-2.0075)}, two of which are complex.

If we reject complex roots  
we are left with the real solutions {(3.0302, 2.0075), (3.0302, -2.0075)}