First factor out $\displaystyle-{16}\usepackage{cmbright}\Huge\$ : $\displaystyle-{16}{\left({{t}}^{{2}}-{25}\right)}={0}\usepackage{cmbright}\Huge\$

This is the difference of two squares, so factor and solve.

$\displaystyle{t}-{5}={0}\usepackage{cmbright}\Huge\$ or $\displaystyle{t}+{5}={0}\usepackage{cmbright}\Huge\$

$\displaystyle{t}={5}\usepackage{cmbright}\Huge\$ or $\displaystyle{t}=-{5}\usepackage{cmbright}\Huge\$

The object will hit the ground in 5 seconds. Since time cannot be negative, $\displaystyle-{5}\usepackage{cmbright}\Huge\$ is not a solution.