Solve fx^2-3x-18=0

$$f x ^ { 2 } - 3 x - 18 = 0$$

Solve for f

$$f=\frac{3\left(x+6\right)}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$fx^{2}-18=3x$$

Add 18 to both sides.

$$fx^{2}=3x+18$$

The equation is in standard form.

$$x^{2}f=3x+18$$

Divide both sides by x^{2}.

$$\frac{x^{2}f}{x^{2}}=\frac{3x+18}{x^{2}}$$

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

$$f=\frac{3x+18}{x^{2}}$$

Divide 18+3x by x^{2}.

$$f=\frac{3\left(x+6\right)}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{3\left(\sqrt{8f+1}+1\right)}{2f}\text{; }x=\frac{3\left(-\sqrt{8f+1}+1\right)}{2f}\text{, }&f\neq 0\\x=-6\text{, }&f=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{3\left(\sqrt{8f+1}+1\right)}{2f}\text{; }x=\frac{3\left(-\sqrt{8f+1}+1\right)}{2f}\text{, }&f\neq 0\text{ and }f\geq -\frac{1}{8}\\x=-6\text{, }&f=0\end{matrix}\right.$$