Answer
Foci: $(-2, -1)$ and $(6, -1)$.
Work Step by Step
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On the LHS, gather all terms containing x:
$9x^{2}-36x=$
$=9(x^{2}-4x)$=$9(x^{2}-4x+4-4)$
$9(x-2)^{2}-36$
...gather the terms containing y:
$25y^{2}+50y=$
$=25(y^{2}+2y)=25(y^{2}+2y+1-1)$
$=25(y+1)^{2}-25$
Rewrite the equation, transferring the constants to the RHS:
$9(x-2)^{2}+25(y+1)^{2}=164+36+25$
$9(x-2)^{2}+25(y+1)^{2}=225\qquad/\div 225$
$\displaystyle \frac{(x-2)^{2}}{25}+\frac{(y+1)^{2}}{9}=1$
$\displaystyle \frac{(x-2)^{2}}{5^{2}}+\frac{(y+1)^{2}}{3^{2}}=1$
major axis horizontal, center at (2,-1),
$a=5,\ b=3$
$c^{2}=a^{2}-b^{2}=25-9=16$
$c=4$
Foci are $c$ units right and $c$ units left of center.
Foci: $(-2, -1)$ and $(6, -1)$.
