Solve the following equation for t . $$ s=\frac{1}{14} \mathrm{gt}^{2} $$

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Solve the equation $$ s=\frac{1}{14} \cdot g \cdot t^{2} $$.
Solve the equation by following steps:
- step0: Solve for $$t$$:
  $$s=\frac{1}{14}gt^{2}$$
- step1: Swap the sides:
  $$\frac{1}{14}gt^{2}=s$$
- step2: Divide both sides:
  $$\frac{\frac{1}{14}gt^{2}}{\frac{1}{14}g}=\frac{s}{\frac{1}{14}g}$$
- step3: Divide the numbers:
  $$t^{2}=\frac{14s}{g}$$
- step4: Simplify the expression:
  $$t=\pm \sqrt{\frac{14s}{g}}$$
- step5: Simplify:
  $$t=\pm \frac{\sqrt{14sg}}{g}$$
- step6: Separate into possible cases:
  $$\begin{align}&t=\frac{\sqrt{14sg}}{g}\&t=-\frac{\sqrt{14sg}}{g}\end{align}$$
The solution to the equation $$ s=\frac{1}{14} \cdot g \cdot t^{2} $$ for $$ t $$ is:

$$ t = \frac{\sqrt{14sg}}{g} $$

or

$$ t = -\frac{\sqrt{14sg}}{g} $$
$$ t = \frac{\sqrt{14sg}}{g} $$ or $$ t = -\frac{\sqrt{14sg}}{g} $$

Solve the following equation for t .

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