Solve 1/2gt^2+frac{3sqrt{59R}}{10}t-9/5R=0

$$\frac{ 1 }{ 2 } g { t }^{ 2 } + \frac{ 3 \sqrt{ 59R } }{ 10 } t- \frac{ 9 }{ 5 } R = 0$$

Solve for g

$$\left\{\begin{matrix}g=-\frac{3\sqrt{59R}}{5t}+\frac{18R}{5t^{2}}\text{, }&t\neq 0\text{ and }R\geq 0\\g\in \mathrm{R}\text{, }&R=0\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 2,10,5.

$$5gt^{2}+3\sqrt{59R}t-18R=0$$

Subtract 3\sqrt{59R}t from both sides. Anything subtracted from zero gives its negation.

$$5gt^{2}-18R=-3\sqrt{59R}t$$

Add 18R to both sides.

$$5gt^{2}=-3\sqrt{59R}t+18R$$

The equation is in standard form.

$$5t^{2}g=-3\sqrt{59R}t+18R$$

Divide both sides by 5t^{2}.

$$\frac{5t^{2}g}{5t^{2}}=\frac{-3\sqrt{59R}t+18R}{5t^{2}}$$

Dividing by 5t^{2} undoes the multiplication by 5t^{2}.

$$g=\frac{-3\sqrt{59R}t+18R}{5t^{2}}$$

Solve for R

$$\left\{\begin{matrix}R=\frac{\left(20g+\sqrt{59\left(40g+59\right)}+59\right)t^{2}}{72}\text{, }&g\geq -\frac{59}{40}\text{ and }t>0\\R=-\frac{\left(-20g+\sqrt{59\left(40g+59\right)}-59\right)t^{2}}{72}\text{, }&\left(g\geq 0\text{ and }t<0\right)\text{ or }\left(g\leq 0\text{ and }g\geq -\frac{59}{40}\text{ and }t>0\right)\\R=0\text{, }&\sqrt{59}t=0\end{matrix}\right.$$