Answer
See graph and explanations.
Work Step by Step
Step 1. Rewrite the equation as $6y^2+(4x)y+(3x^2-7)$ and let $a=6, b=4x, c=3x^2-7$
Step 2. Use the quadratic formula $y=\frac{-b\pm\sqrt {b^2-4ac}}{2a}$ to get $y=\frac{-4x\pm\sqrt {(4x)^2-4(6)(3x^2-7)}}{12}=\frac{-2x\pm\sqrt {42-14x^2}}{6}$
Step 3. We can graph the equations $y_1=\frac{-2x+\sqrt {42-14x^2}}{6}$ and $y_2=\frac{-2x-\sqrt {42-14x^2}}{6}$ as shown in the figure.
