The equation provided is:

$3 = N g^2 - Q$

We are tasked with solving for $g$, assuming all variables are positive and not using any absolute values or signs. Here is how we can solve the equation:

Step 1: Isolate the $g^2$ term.

$N g^2 = 3 + Q$

Step 2: Solve for $g^2$.

$g^2 = \frac{3 + Q}{N}$

Step 3: Solve for $g$.

Since all variables are positive, we can take the positive square root: $g = \sqrt{\frac{3 + Q}{N}}$

Thus, the solution for $g$ is:

$g = \sqrt{\frac{3 + Q}{N}}$

Would you like more details on any of the steps?

Related Questions:

1. How can this equation be applied in physics or engineering problems?
2. What if one of the variables $N$ or $Q$ were zero? How would the solution change?
3. How do we solve a similar equation where $N$, $Q$, or the constant term changes?
4. What happens if the assumption of positivity is removed and negative roots are considered?
5. How can we check if the derived solution is correct by substituting back into the original equation?

Tip:

When solving quadratic equations, always check the assumptions on the variables, such as positivity, as they can simplify the solution process and avoid unnecessary consideration of extraneous solutions.