Final answer:
To solve the quadratic equation P(q) = -4q²+ 181q - 590, use the quadratic formula and substitute the values of a, b, and c. Solve the equation to find the solutions for q.
Step-by-step explanation:
This expression is a quadratic equation of the form P(q) = -4q²+ 181q - 590. To solve this equation, we will use the quadratic formula. The values of a, b, and c are -4, 181, and -590 respectively.
Using the quadratic formula, q = (-b ± sqrt(b² - 4ac)) / (2a). Plugging in the values, we get q = (-181 ± sqrt(181² - 4*(-4)*(-590))) / (2*(-4)). Solving this equation will give us the solutions for q.