The curve below has a horizontal tangent line at the point (4,7)\displaystyle {\left(-{4},{7}\right)} and at one other point. Find the coordinates of the second point where the curve has a horizontal tangent line.

25x2+200x+4y216y=316\displaystyle {25}{x}^{{2}}+{200}{x}+{4}{y}^{{2}}-{16}{y}=-{316}

x\displaystyle {x}-coordinate of second point =  

y\displaystyle {y}-coordinate of second point =