If the domain of the function \( \log_{5}(18x-x^{2}-77) \) is \( (\alpha,\beta) \) and the domain of the function \(\displaystyle \log_{(x-1)}\!\left(\frac{2x^{2}+3x-2}{x^{2}-3x-4}\right) \) is \( (\gamma,\delta) \), then \( \alpha^{2}+\beta^{2}+\gamma^{2} \) is equal to:
