If the equation a ( b - c ) x^2+ b ( c - a ) x + c ( a - b )=0 has equal roots, where a + c =15 and b =36/5, then a^2+ c^2 is equal to ____

If the equation $\displaystyle \mathrm{a}(\mathrm{b}-\mathrm{c}) \mathrm{x}^2+\mathrm{b}(\mathrm{c}-\mathrm{a}) \mathrm{x}+\mathrm{c}(\mathrm{a}-\mathrm{b})=0$ has equal roots, where $\displaystyle \mathrm{a}+\mathrm{c}=15$ and $\displaystyle \mathrm{b}=\frac{36}{5}$, then $\displaystyle \mathrm{a}^2+\mathrm{c}^2$ is equal to $\displaystyle \_\_\_\_$