The height is given by the expression
[tex]h=4+40t-16t^2[/tex]
We want to solve that equation for h = 26 feet.
[tex]\begin{gathered} 26=4+40t-16t^2 \\ \\ -16t^2+40t-22=0 \end{gathered}[/tex]
Then we must solve the quadratic:
[tex]-16t^2+40t-22=0[/tex]
Using the quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}{}}{2a}[/tex]
Where a = -16, b = 40 and c = -22
[tex]\begin{gathered} t=\frac{-b\pm\sqrt[]{b^2-4ac}{}}{2a} \\ \\ t=\frac{-40\pm\sqrt[]{(40)^2-4\cdot(-16)(-22)}{}}{2\cdot(-16)} \\ \\ t=\frac{-40\pm\sqrt[]{1600-1408}{}}{-32} \\ \\ t=\frac{-40\pm\sqrt[]{192}{}}{-32}=\frac{40\pm8\sqrt[]{3}{}}{32}=\frac{5}{4}\pm\frac{\sqrt{3}{}}{4} \end{gathered}[/tex]
Therefore the solutions are
[tex]t_1=\frac{5}{4}+\frac{\sqrt[]{3}}{4}\text{ and }t_2=\frac{5}{4}-\frac{\sqrt[]{3}}{4}[/tex]
If we write it in decimal, we get
[tex]\begin{gathered} t_1=1.68\text{ seconds} \\ t_2=0.82\text{ seconds} \end{gathered}[/tex]
