You need to solve the equation: $\displaystyle{6}=-{16}{{t}}^{{2}}+{70}{t}+{4}\usepackage{cmbright}\Huge\$

Rewrite in standard form: $\displaystyle{16}{{t}}^{{2}}-{70}{t}+{2}={0}\usepackage{cmbright}\Huge\$

Use the Quadratic Formula: $\displaystyle{t}=\frac{{-{\left(-{70}\right)}\pm\sqrt{{{{\left(-{70}\right)}}^{{2}}-{4}\cdot{16}\cdot{2}}}}}{{{2}\cdot{16}}}\usepackage{cmbright}\Huge\$

Simplify: $\displaystyle{t}=\frac{{{70}\pm\sqrt{{4772}}}}{{32}}\approx\frac{{{70}\pm{69.08}}}{{32}}\usepackage{cmbright}\Huge\$

The smaller solution ( $\displaystyle{t}\approx{0.03}\usepackage{cmbright}\Huge\$ ) is when the ball is going up. The larger solution, $\displaystyle{t}\approx{4.35}\usepackage{cmbright}\Huge\$ seconds, is the answer.