The given quadratic equation is
[tex]0=-16x^2+64x+80[/tex]
At first switch the 2 sides
[tex]-16x^2+64x+80=0[/tex]
Divide all terms by -16 to simplify it
[tex]\begin{gathered} \frac{-16x^2}{-16}+\frac{64x}{-16}+\frac{80}{-16}=\frac{0}{-16} \\ \\ x^2-4x-5=0 \end{gathered}[/tex]
Now, we need to factor the lift side
[tex]\begin{gathered} x^2=(x)(x) \\ -5=(1)(-5) \\ (x)(1)+(x)(-5)=x-5x=-4x \\ x^2-4x-5=(x+1)(x-5) \end{gathered}[/tex]
Then the equation is
[tex](x+1)(x-5)=0[/tex]
Equate each factor by 0 to find x
[tex]\begin{gathered} x+1=0 \\ x+1-1=0-1 \\ x=-1 \end{gathered}[/tex][tex]\begin{gathered} x-5=0 \\ x-5+5=0+5 \\ x=5 \end{gathered}[/tex]
Since the time can not be a negative value, then we will refuse x = -1
The stick hit the ground after 5 seconds
