The foci of the hyperbola $5{\mathrm{x}}^2-6{\mathrm{y}}^2-10\mathrm{x}-24\mathrm{y}-34=0\text{ are }$

$\begin{array}{l}5{\mathrm{x}}^2-6{\mathrm{y}}^2-10\mathrm{x}-24\mathrm{y}-34=0\\ 5\left({\mathrm{x}}^2-2\mathrm{x}\right)-6\left({\mathrm{y}}^2+4\mathrm{y}\right)=34\\ 5\left({\mathrm{x}}^2-2\mathrm{x}+1\right)-6\left({\mathrm{y}}^2+4\mathrm{y}+4\right)=34+5-24\\ 5(\mathrm{x}-1{)}^2-6(\mathrm{y}+2{)}^2=15\\ \frac{(\mathrm{x}-1{)}^2}{\frac{15}{5}}-\frac{(\mathrm{y}+2{)}^2}{\frac{15}{6}}=1\\ \begin{array}{l}\mathrm{a}=\sqrt{\frac{15}{5}},\mathrm{b}=\sqrt{\frac{15}{6}}\\ \mathrm{e}=\sqrt{\frac{17}{6}}\\ \therefore \text{ foci are }(1\pm \mathrm{ae},-2)\\ =\left(1\pm \sqrt{3}\cdot \frac{\sqrt{11}}{\sqrt{6}},-2\right)\\ =\left(1\pm \sqrt{\frac{11}{2}},-2\right)\end{array}\end{array}$