The equation 0=−(4.90 m/s^2)t^2 -(8.00 m/s)t + 30m is a quadratic equation that needs to be solved for time, t. The coefficients for the quadratic formula are identified as a = -4.90, b = -8.00, and c = 30. The discussion highlights that the determinant is positive, indicating two distinct real roots for t. A clarification is provided on calculating the determinant, confirming it yields a real number. The conversation emphasizes the use of the quadratic formula to find the solutions for t.