problem: The equation $y = -16t^2 + 26t + 105$ describes the height (in feet) of a ball tossed up in the air at 26 feet per second from a height of 105 feet above the ground. In how many seconds will the ball hit the ground? Express your answer as a decimal rounded to the nearest tenth.
solution: Setting $y$ to zero, we find the following: \begin{align*}
  0& = -16t^2 + 26t + 105\\
  & = 16t^2 - 26t - 105\\
  & = (8t + 15)(2t - 7)
  \end{align*}As $t$ must be positive, we can see that $t = \frac{7}{2} = \boxed{3.5}.$