Solve for g 3=Ng^2-Q

$3 = N g^{2} - Q$

Rewrite the equation as $N g^{2} - Q = 3$ .

$N g^{2} - Q = 3$

Add $Q$ to both sides of the equation.

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

Divide each term in $N g^{2} = 3 + Q$ by $N$ and simplify.

Divide each term in $N g^{2} = 3 + Q$ by $N$ .

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

Simplify the left side.

Cancel the common factor of $N$ .

Cancel the common factor.

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

Divide $g^{2}$ by $1$ .

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

Take the square root of both sides of the equation to eliminate the exponent on the left side.

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

Simplify $\pm \sqrt{\frac{3}{N} + \frac{Q}{N}}$ .

Combine the numerators over the common denominator.

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

Rewrite $\sqrt{\frac{3 + Q}{N}}$ as $\frac{\sqrt{3 + Q}}{\sqrt{N}}$ .

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

Multiply $\frac{\sqrt{3 + Q}}{\sqrt{N}}$ by $\frac{\sqrt{N}}{\sqrt{N}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{\sqrt{3 + Q}}{\sqrt{N}}$ by $\frac{\sqrt{N}}{\sqrt{N}}$ .

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

Raise $\sqrt{N}$ to the power of $1$ .

$g = \pm \frac{\sqrt{3 + Q} \sqrt{N}}{{\sqrt{N}}^{1} \sqrt{N}}$

Raise $\sqrt{N}$ to the power of $1$ .

$g = \pm \frac{\sqrt{3 + Q} \sqrt{N}}{{\sqrt{N}}^{1} {\sqrt{N}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$g = \pm \frac{\sqrt{3 + Q} \sqrt{N}}{{\sqrt{N}}^{1 + 1}}$

Add $1$ and $1$ .

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

Rewrite ${\sqrt{N}}^{2}$ as $N$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{N}$ as $N^{\frac{1}{2}}$ .

$g = \pm \frac{\sqrt{3 + Q} \sqrt{N}}{{(N^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$g = \pm \frac{\sqrt{3 + Q} \sqrt{N}}{N^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$g = \pm \frac{\sqrt{3 + Q} \sqrt{N}}{N^{1}}$

Simplify.

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

Combine using the product rule for radicals.

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

Reorder factors in $\pm \frac{\sqrt{(3 + Q) N}}{N}$ .

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

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

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

Next, use the negative value of the $\pm$ to find the second solution.

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

The complete solution is the result of both the positive and negative portions of the solution.

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

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

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

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

Solve for g 3=Ng^2-Q

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