Chapter 11 - Quadratic Functions and Equations - 11.4 Applications Involving Quadratic Equations - 11.4 Exercise Set - Page 724: 21

$\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$.

$a{{t}^{2}}+bt+c=0$ Since this equation is a quadratic equation, we can use the quadratic formula. $t=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ Thus the value is $t=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$.