Math Snap

STEP 1

1. All variables, including $A$, are positive.
2. We are solving for $A$ in terms of the other variables.
3. The equation is a polynomial equation in terms of $A$.

STEP 2

1. Isolate the term containing $A$.
2. Solve for $A$ by taking the square root.

STEP 3

Start by isolating the term containing $A$. We want to move all other terms to the opposite side of the equation. Add $G$ to both sides:
$$5h^3 = bA^2 - G$$ $$5h^3 + G = bA^2$$

STEP 4

Now, solve for $A^2$ by dividing both sides by $b$:
$$bA^2 = 5h^3 + G$$ $$A^2 = \frac{5h^3 + G}{b}$$

Finally, solve for $A$ by taking the square root of both sides. Since all variables are positive, we do not need to consider the negative root:
$$A = \sqrt{\frac{5h^3 + G}{b}}$$ The solution for $A$ is:
$$A = \sqrt{\frac{5h^3 + G}{b}}$$