Final answer:
A quadratic equation is characterized by the standard form at² + bt + c = 0. To solve it, the quadratic formula √(b² - 4ac)/2a is utilized, and with constants a = 4.90, b = 14.3, and c = -20.0, the formula yields the solutions after calculating the discriminant and evaluating the roots.
Step-by-step explanation:
Understanding Quadratic Equations
A quadratic equation is an expression of the form at² + bt + c = 0, where a, b, and c are constants. To solve for the variable t, the quadratic formula is used, which is √(b² - 4ac)/2a. For the given quadratic equation with constants a = 4.90, b = 14.3, and c = -20.0, we can substitute these into the quadratic formula to find the solutions for t.
The general process involves calculating the discriminant b² - 4ac, then determining the two possible values for t by adding or subtracting the square root of the discriminant from -b and finally dividing by 2a. This procedure provides the solutions which are the points where the quadratic equation crosses the t-axis when graphed.