The given equation for the area of a circle in terms of the diameter $d$ is:

$A = \frac{\pi d^2}{4}$

To isolate $d$, follow these steps:

1. Multiply both sides by 4 to eliminate the fraction:

   $4A = \pi d^2$

2. Divide both sides by $\pi$:

   $\frac{4A}{\pi} = d^2$

3. Take the square root of both sides:

   $d = \sqrt{\frac{4A}{\pi}}$

Thus, the equation solved for $d$ is:

$d = \frac{2\sqrt{A}}{\sqrt{\pi}}$

Would you like a step-by-step breakdown with an example?

Here are some related questions to explore further:

1. How is this formula derived from the standard area formula $A = \pi r^2$?
2. What is the relationship between the radius and diameter in a circle?
3. If the area of a circle is given, how can you find its radius directly?
4. How does this formula change if solving for the radius $r$ instead?
5. Can this equation be used in real-world applications like calculating the size of circular objects?

Tip: Remember that the diameter is always twice the radius: $d = 2r$.