It would take 9 seconds.
Substituting the values into the equation, we have:
0 = -16t² + 138t + 55
The quadratic formula is:
[tex]t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Inserting our information we have:
[tex]t=\frac{-138\pm \sqrt{138^2-4(-16)(55)}}{2(-16)}
\\
\\=\frac{-138\pm \sqrt{19044--3520}}{-32}
\\
\\=\frac{-138\pm \sqrt{19044+3520}}{-32}
\\
\\=\frac{-138\pm \sqrt{22564}}{-32}
\\
\\=\frac{-138\pm 150}{-32}=\frac{-138+150}{-32}\text{ or } \frac{-138-150}{-32}
\\
\\=\frac{12}{-32}\text { or } \frac{288}{32}=-0.375 \text{ or } 9[/tex]
