Final answer:
The student's query points to solving a quadratic equation using a, b, and c values in the quadratic formula. However, the expressions given in the question seem unrelated, likely due to typos within the question text.
Step-by-step explanation:
The student's question appears to contain elements of a mathematical quadratic equation, which is represented by the form at² + bt + c = 0. To solve a quadratic equation when the constants are given, one would use the quadratic formula: x = −b ± √(b² − 4ac) / (2a). The coefficients a, b, and c represent distinct elements of the equation, such as the quadratic coefficient, the linear coefficient, and the constant term, respectively.
It seems like the student's question may have some missing parts, as the expressions (3/8)-:(13/12) and (3/8)*(a/b) do not directly relate to the quadratic formula mentioned. If the values for a, b, and c are respectively given as 4.90, −14.3, and −20.0, then these would be substituted into the quadratic formula to find the solution for the variable t.
Note that the typos, such as 'expressions: (3)/(8)-:(13)/(12) and (3)/(8)*(a)/(b) he value of b, separated by a comma,' seem to imply a formula or an expression that isn't immediately relevant to the quadratic equation presented.