Answer
See graph and explanations.
Work Step by Step
Step 1. Rewrite the equation as
$3y^2-(6x+8)y+(3x^2+10x-2)$
and let
$a=3, b=-(6x+8), c=3x^2+10x-2$
Step 2. Use the quadratic formula
$y=\frac{-b\pm\sqrt {b^2-4ac}}{2a}$ to get $y=\frac{6x+8\pm\sqrt {(6x+8)^2-4(3)(3x^2+10x-2)}}{6}=\frac{3x+4\pm\sqrt {22-6x}}{3}$
Step 3. We can graph the equations $y_1=\frac{3x+4+\sqrt {22-6x}}{3}$ and $y_2=\frac{3x+4-\sqrt {22-6x}}{3}$ as shown in the figure.
