Final answer:
To solve the equation 3b² - 128 = -8b, use the quadratic formula to find the solutions.
Step-by-step explanation:
To solve the equation 3b² - 128 = -8b, we need to manipulate it so that it is in the form ax² + bx + c = 0. Moving all the terms to one side, we get 3b² + 8b - 128 = 0. Now, we can use the quadratic formula -b ± √(b² - 4ac) / 2a to find the solutions of the quadratic equation.
For this equation, a = 3, b = 8, and c = -128. Plugging these values into the quadratic formula, we get:
b = -8 ± √((-8)² - 4(3)(-128)) / (2)(3).
Simplifying further, we have b = -8 ± √(64 + 1536) / 6.
b = -8 ± √(1600) / 6.
b = -8 ± 40 / 6.
Therefore, the solutions to the equation 3b² - 128 = -8b are b = -8 + 40/6 and b = -8 - 40/6.