Final answer:
The value of c in the quadratic equation at² + bt + c = 0 provided in the question is -20.0. There's no need to apply the quadratic formula as c is already given.
Step-by-step explanation:
The initial question mentions an equation of the form at² + bt + c = 0, with constants a = 4.90, b = 14.3, and c = -20.0. To find the solutions for t, the quadratic formula is applied, which is t = (-b ± √(b² - 4ac)) / (2a). However, since the query asks for the final value of c, which is already given as -20.0, there is no need to use the quadratic formula for this purpose. Instead, we directly know that the value of c in the quadratic equation provided is -20.0.