SOLUTION
From the question, the ball's height in meters is represented by the equation

Now we are told to find all values of t, for which the ball's height is 12 meters.
This means that h = 12 meters.
So that means

So now solving the quadratic equation for t, we have
![\begin{gathered} t^2-5t+2=0 \\ t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{Where a = 1, b = -5, c =2 } \\ t=\frac{-(-5\pm\sqrt[]{(-5)^2-4*1*2}}{2*1} \\ t=\frac{5\pm\sqrt[]{17}}{2} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/xbx5y4lw5oewr9zr2huwdn6nyhm4hbm5y7.png)
So, either
![\begin{gathered} t=\frac{5+\sqrt[]{17}}{2} \\ t=4.56155281 \\ t=4.56\sec s \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/l8lfn3a7b1vkhx1iq52z0zpjpz0d038tta.png)
Or
![\begin{gathered} t=\frac{5-\sqrt[]{17}}{2} \\ t=0.43844718 \\ t=0.44\sec s\text{ } \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/6q2j9vwkwsrqfe38ahdc3sanx49o92l9j9.png)
Hence the answer is t = 4.56 secs or 0.44 secs