Chapter 10 - Exponents and Radicals - 10.6 Solving Radical Equations - 10.6 Exercise Set - Page 669: 71

$$ t=\frac{245700S^2-309614990593}{1064782161}$$

We solve for $t$ as the problems asks us to do: $$1087.7\sqrt{\frac{9t+2617}{2457}}=S\\ \left(\sqrt{\frac{9t+2617}{2457}}\right)^2=\left(\frac{S\cdot \:10}{10877}\right)^2\\ t=\frac{245700S^2-309614990593}{1064782161}$$