Solve 0.9a=1/2gt^2

$$0.9 a = \frac { 1 } { 2 } g t ^ { 2 }$$

Solve for a

$$a=\frac{5gt^{2}}{9}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$0.9a=\frac{gt^{2}}{2}$$

Divide both sides of the equation by 0.9, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.9a}{0.9}=\frac{gt^{2}}{0.9\times 2}$$

Dividing by 0.9 undoes the multiplication by 0.9.

$$a=\frac{gt^{2}}{0.9\times 2}$$

Divide \frac{gt^{2}}{2} by 0.9 by multiplying \frac{gt^{2}}{2} by the reciprocal of 0.9.

$$a=\frac{5gt^{2}}{9}$$

Solve for g

$$\left\{\begin{matrix}g=\frac{9a}{5t^{2}}\text{, }&t\neq 0\\g\in \mathrm{R}\text{, }&a=0\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}gt^{2}=0.9a$$

The equation is in standard form.

$$\frac{t^{2}}{2}g=\frac{9a}{10}$$

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

$$\frac{2\times \frac{t^{2}}{2}g}{t^{2}}=\frac{9a}{10\times \frac{t^{2}}{2}}$$

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

$$g=\frac{9a}{10\times \frac{t^{2}}{2}}$$

Divide \frac{9a}{10} by \frac{1}{2}t^{2}.

$$g=\frac{9a}{5t^{2}}$$