"Solve the following system of equations symbolically"

I need a bit of help, here. My homework says

"Solve the following system of equations symbolically:

y=2x²-3 and x²+y² = 16"

y = 2x² - 3 is a parabola (quadratic form)
x² + y² = 16 is a circle centered at (0 , 0) with a radius of r = 4

the parabola will intersect this circle at two points

to solve "symbolically"
x² + y² = 16
2x² + 2y² = 32
but y = 2x² - 3
hence
y + 3 + 2y² = 32
or
2y² + y + 3 = 32
or
2y² + y - 29 = 0
which is a quadratic equation having roots
y = -0.25 + sqrt(233) / 4
and
y = -0.25 - sqrt(233) / 4

since
y = 2x² - 3 or x = +sqrt[(y + 3) / 2] and x = -sqrt[(y + 3) / 2]
we can then back substitute to find the associated x - values for each of the above solutions

for y = -0.25 + sqrt(233) / 0.25
x = +sqrt[(y + 3) / 2] and x = -sqrt[(y + 3) / 2] become
x = +sqrt[(-0.25 + sqrt(233) / 4 + 3) / 2] and x = -sqrt[(-0.25 + sqrt(233) / 4 + 3) / 2] or
x = +1.8119 and x = -1.8119
hence the two intersection points are:
(1.8119 , -0.25 + sqrt(233) / 4) and (-1.8119 , -0.25 + sqrt(233) / 4)

for y = -0.25 - sqrt(233)
we arrive at imaginary solutions that we discard