Answer
See graph and explanations.
Work Step by Step
Step 1. Rewrite the equation as
$16y^2+(24x-130)y+(9x^2+90x)$
and let $a=16, b=24x-130, c=9x^2+90x$
Step 2. Use the quadratic formula $y=\frac{-b\pm\sqrt {b^2-4ac}}{2a}$ to get
$y=\frac{-24x+130\pm\sqrt {(24x-130)^2-4(16)(9x^2+90x)}}{32}=\frac{-12x+65\pm\sqrt {(12x-65)^2-16(9x^2+90x)}}{16}$
Step 3. We can graph the equations
$y_1=\frac{-12x+65+\sqrt {(12x-65)^2-16(9x^2+90x)}}{16}$
and
$y_2=\frac{-12x+65-\sqrt {(12x-65)^2-16(9x^2+90x)}}{16}$
as shown in the figure.
