Solve 10=1/2gt^2

$$10 = \frac { 1 } { 2 } g t ^ { 2 }$$

Solve for g

$$g=\frac{20}{t^{2}}$$

$$t\neq 0$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{2}gt^{2}=10$$

The equation is in standard form.

$$\frac{t^{2}}{2}g=10$$

Divide both sides by \frac{1}{2}t^{2}.

$$\frac{2\times \frac{t^{2}}{2}g}{t^{2}}=\frac{2\times 10}{t^{2}}$$

Dividing by \frac{1}{2}t^{2} undoes the multiplication by \frac{1}{2}t^{2}.

$$g=\frac{2\times 10}{t^{2}}$$

Divide 10 by \frac{1}{2}t^{2}.

$$g=\frac{20}{t^{2}}$$

Solve for t (complex solution)

$$t=-2\sqrt{5}g^{-\frac{1}{2}}$$

$$t=2\sqrt{5}g^{-\frac{1}{2}}\text{, }g\neq 0$$

Solve for t

$$t=2\sqrt{\frac{5}{g}}$$

$$t=-2\sqrt{\frac{5}{g}}\text{, }g>0$$