Answer:
[tex]t \approx 4.501\,s[/tex]
Step-by-step explanation:
The second-grade equation must be rearragend into its standard form:
[tex]-16\cdot t^{2} + 70\cdot t + 9 = 0[/tex]
Roots can be found with the help of the General Equation for Second-Order Polynomial:
[tex]t = \frac{-70\pm \sqrt{70^{2}-4\cdot (-16)\cdot (9)}}{2\cdot (-16)}[/tex]
[tex]t = 2.188 \pm 2.313[/tex]
[tex]t_{1} \approx 4.501\,s[/tex]
[tex]t_{2} \approx -0.125\,s[/tex]
Only the first root offers a reasonable solution.
[tex]t \approx 4.501\,s[/tex]
