You need to solve the equation: $\displaystyle{0}=-{16}{{t}}^{{2}}+{25}{t}+{5}\usepackage{cmbright}\Huge\$

Rewrite in standard form: $\displaystyle{16}{{t}}^{{2}}-{25}{t}-{5}={0}\usepackage{cmbright}\Huge\$

Use the Quadratic Formula: $\displaystyle{t}=\frac{{-{\left(-{25}\right)}\pm\sqrt{{{{\left(-{25}\right)}}^{{2}}-{4}\cdot{16}\cdot{\left(-{5}\right)}}}}}{{{2}\cdot{16}}}\usepackage{cmbright}\Huge\$

Simplify: $\displaystyle{t}=\frac{{{25}\pm\sqrt{{945}}}}{{32}}\approx\frac{{{25}\pm{30.74}}}{{32}}\usepackage{cmbright}\Huge\$

The smaller solution ( $\displaystyle{t}\approx-{0.18}\usepackage{cmbright}\Huge\$ ) cannot be the time because it is a negative number. The larger solution, $\displaystyle{t}\approx{1.74}\usepackage{cmbright}\Huge\$ seconds, is the answer.