Solve fm^2-3m-10=0?

$$f m ^ { 2 } - 3 m - 10 = 0 ?$$

Solve for f

$$f=\frac{3m+10}{m^{2}}$$

$$m\neq 0$$

Steps for Solving Linear Equation

Add 3m to both sides. Anything plus zero gives itself.

$$fm^{2}-10=3m$$

Add 10 to both sides.

$$fm^{2}=3m+10$$

The equation is in standard form.

$$m^{2}f=3m+10$$

Divide both sides by m^{2}.

$$\frac{m^{2}f}{m^{2}}=\frac{3m+10}{m^{2}}$$

Dividing by m^{2} undoes the multiplication by m^{2}.

$$f=\frac{3m+10}{m^{2}}$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{\sqrt{40f+9}+3}{2f}\text{; }m=\frac{-\sqrt{40f+9}+3}{2f}\text{, }&f\neq 0\\m=-\frac{10}{3}\text{, }&f=0\end{matrix}\right.$$

Solve for m

$$\left\{\begin{matrix}m=\frac{\sqrt{40f+9}+3}{2f}\text{; }m=\frac{-\sqrt{40f+9}+3}{2f}\text{, }&f\neq 0\text{ and }f\geq -\frac{9}{40}\\m=-\frac{10}{3}\text{, }&f=0\end{matrix}\right.$$