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