Solve ny=1.5+40t-10t^2

$$n y = 1.5 + 40 t - 10 t ^ { 2 }$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=-\frac{10t^{2}-40t-1.5}{y}\text{, }&y\neq 0\\n\in \mathrm{C}\text{, }&\left(t=-\frac{\sqrt{415}}{10}+2\text{ or }t=\frac{\sqrt{415}}{10}+2\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$yn=1.5+40t-10t^{2}$$

Divide both sides by y.

$$\frac{yn}{y}=\frac{1.5+40t-10t^{2}}{y}$$

Dividing by y undoes the multiplication by y.

$$n=\frac{1.5+40t-10t^{2}}{y}$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{10t^{2}-40t-1.5}{y}\text{, }&y\neq 0\\n\in \mathrm{R}\text{, }&\left(t=-\frac{\sqrt{415}}{10}+2\text{ or }t=\frac{\sqrt{415}}{10}+2\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$yn=1.5+40t-10t^{2}$$

Divide both sides by y.

$$\frac{yn}{y}=\frac{1.5+40t-10t^{2}}{y}$$

Dividing by y undoes the multiplication by y.

$$n=\frac{1.5+40t-10t^{2}}{y}$$

Solve for t (complex solution)

$$t=-\frac{\sqrt{415-10ny}}{10}+2$$

$$t=\frac{\sqrt{415-10ny}}{10}+2$$

Solve for t

$$t=-\frac{\sqrt{415-10ny}}{10}+2$$

$$t=\frac{\sqrt{415-10ny}}{10}+2\text{, }\left(y\geq 0\text{ or }n\geq \frac{83}{2y}\right)\text{ and }\left(y\leq 0\text{ or }n\leq \frac{83}{2y}\right)$$