Solve the formula b=−8y−3aa𝑏=-8𝑦-3𝑎𝑎 for a𝑎 .a𝑎 =  Enter your answer as an expression.

1. Break Down the Problem

We need to isolate $a$ in the equation $b = -8y - 3a^2$.

2. Relevant Concepts

To isolate $a$, we will rearrange the equation and solve for $a$. This involves moving terms around and applying algebraic manipulation.

3. Analysis and Detail

Starting with the original equation: $b = -8y - 3a^2$

1. Add $3a^2$ to both sides: $b + 3a^2 = -8y$
2. Subtract $b$ from both sides: $3a^2 = -8y - b$
3. Divide each side by 3: $a^2 = \frac{-8y - b}{3}$
4. Take the square root of both sides to solve for $a$: $a = \pm \sqrt{\frac{-8y - b}{3}}$

4. Verify and Summarize

We have isolated $a$ in terms of $y$ and $b$. The expression provides both positive and negative potential values for $a$, reflecting that both square roots are valid.

Final Answer

$a = \pm \sqrt{\frac{-8y - b}{3}}$