Final answer:
The student's question mixes elements of absolute value, linear, and quadratic equations, but the provided solution seems to be a point rather than a quadratic solution. To solve a quadratic equation of the form at² + bt + c = 0, the quadratic formula is used with the given coefficients.
Step-by-step explanation:
The question pertains to the types of equations and their solutions. While the student has mentioned an absolute value and a linear equation, they have also presented parameters for a quadratic equation that doesn't seem to directly relate to the initial information given. The quadratic equation is given by the form at² + bt + c = 0, and to find its solutions, you would typically use the quadratic formula. However, the provided solution (-.5, -5) seems to be a point on a graph, which could relate to either a linear or an absolute value equation, but not directly to the quadratic equation provided.
If we were to address the quadratic component mentioned, you could use the given constants (a = 4.90, b = 14.3, c = -20.0) to plug into the quadratic formula. The formula is x = (-b ± √(b² - 4ac))/(2a), where 'x' represents the solutions of the equation, and 'a', 'b', and 'c' are coefficients from the quadratic equation.