Answer
See graph and explanations.
Work Step by Step
Step 1. Rewrite the equation as
$4y^2+(4x)y+(x^2+10\sqrt 5x-9)$
and let
$a=4, b=4x, c=x^2+10\sqrt 5x-9$
Step 2. Use the quadratic formula $y=\frac{-b\pm\sqrt {b^2-4ac}}{2a}$ to get
$y=\frac{-4x\pm\sqrt {(4x)^2-4(4)(x^2+10\sqrt 5x-9)}}{8}=\frac{-x\pm\sqrt {9-10\sqrt 5x}}{2}$
Step 3. We can graph the equations $y_1=\frac{-x+\sqrt {9-10\sqrt 5x}}{2}$ and $y_2=\frac{-x-\sqrt {9-10\sqrt 5x}}{2}$ as shown in the figure.
