solve for t. use the quadratic formula.d=−16t^2+12t

Answer:[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{3+\sqrt{9+4d}}{8}[/tex]Step-by-step explanation:Given: d = -16t² + 12tTo find: t using quadratic formulaIf we have quadratic equation in form ax² + bx + c = 0then, by quadratic formula we have[tex]x\,=\,\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Rewrite the given equation,-16t² + 12t - d = 0from this equation we have,a = -16 , b = 12 , c = dnow using quadratic formula we get,[tex]t\,=\,\frac{-12\pm\sqrt{12^2-4\times(-16)\times d}}{2\times(-16)}[/tex][tex]t\,=\,\frac{-12\pm\sqrt{144+64d}}{-32}[/tex][tex]t\,=\,\frac{-12\pm\sqrt{16(9+4d)}}{-32}[/tex][tex]t\,=\,\frac{-12\pm4\sqrt{9+4d}}{-32}[/tex][tex]t\,=\,\frac{4(-3\pm\sqrt{9+4d})}{-32}[/tex][tex]t\,=\,\frac{-3\pm\sqrt{9+4d}}{-8}[/tex] [tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:,\:\:\frac{-3-\sqrt{9+4d}}{-8}[/tex] [tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{-(3+\sqrt{9+4d})}{-8}[/tex] [tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{3+\sqrt{9+4d}}{8}[/tex]Therefore, [tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{3+\sqrt{9+4d}}{8}[/tex]