Solve {left(t/sqrt{{h_{2}}-sqrt{{h}_{1}}}right)}^2div2/g=1

$${ \left( \frac{ t }{ \sqrt{ { h }_{ 2 } } - \sqrt{ { h }_{ 1 } } } \right) }^{ 2 } \div \frac{ 2 }{ g } = 1$$

Solve for g

$$g=2\times \left(\frac{\sqrt{h_{2}}-\sqrt{h_{1}}}{t}\right)^{2}$$

$$t\neq 0\text{ and }h_{2}\geq 0\text{ and }h_{1}\geq 0\text{ and }h_{2}\neq h_{1}$$

Solve for h_1

$$\left\{\begin{matrix}h_{1}=\frac{\left(\sqrt{g}t+\sqrt{2h_{2}}\right)^{2}}{2}\text{, }&h_{2}\geq 0\text{ and }t\neq -\frac{2\sqrt{2h_{2}}}{\sqrt{g}}\text{ and }\frac{\sqrt{2g}t}{2}+\sqrt{h_{2}}\geq 0\text{ and }t\neq 0\text{ and }g>0\\h_{1}=\frac{\left(-\sqrt{g}t+\sqrt{2h_{2}}\right)^{2}}{2}\text{, }&t\neq \frac{2\sqrt{2h_{2}}}{\sqrt{g}}\text{ and }h_{2}\geq 0\text{ and }-\frac{\sqrt{2g}t}{2}+\sqrt{h_{2}}\geq 0\text{ and }g>0\text{ and }t\neq 0\end{matrix}\right.$$