Solve fx^2-6x+8=0

$$f x ^ { 2 } - 6 x + 8 = 0$$

Solve for f

$$f=-\frac{2\left(4-3x\right)}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Add 6x to both sides. Anything plus zero gives itself.

$$fx^{2}+8=6x$$

Subtract 8 from both sides.

$$fx^{2}=6x-8$$

The equation is in standard form.

$$x^{2}f=6x-8$$

Divide both sides by x^{2}.

$$\frac{x^{2}f}{x^{2}}=\frac{6x-8}{x^{2}}$$

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

$$f=\frac{6x-8}{x^{2}}$$

Divide 6x-8 by x^{2}.

$$f=\frac{2\left(3x-4\right)}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{9-8f}+3}{f}\text{; }x=\frac{-\sqrt{9-8f}+3}{f}\text{, }&f\neq 0\\x=\frac{4}{3}\text{, }&f=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{9-8f}+3}{f}\text{; }x=\frac{-\sqrt{9-8f}+3}{f}\text{, }&f\neq 0\text{ and }f\leq \frac{9}{8}\\x=\frac{4}{3}\text{, }&f=0\end{matrix}\right.$$