Solve c3x-x^2-2=0

$$c 3 x - x ^ { 2 } - 2 = 0$$

Solve for c_3

$$c_{3}=x+\frac{2}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Add x^{2} to both sides. Anything plus zero gives itself.

$$c_{3}x-2=x^{2}$$

Add 2 to both sides.

$$c_{3}x=x^{2}+2$$

The equation is in standard form.

$$xc_{3}=x^{2}+2$$

Divide both sides by x.

$$\frac{xc_{3}}{x}=\frac{x^{2}+2}{x}$$

Dividing by x undoes the multiplication by x.

$$c_{3}=\frac{x^{2}+2}{x}$$

Divide x^{2}+2 by x.

$$c_{3}=x+\frac{2}{x}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{c_{3}^{2}-8}+c_{3}}{2}$$

$$x=\frac{\sqrt{c_{3}^{2}-8}+c_{3}}{2}$$

Solve for x

$$x=\frac{-\sqrt{c_{3}^{2}-8}+c_{3}}{2}$$

$$x=\frac{\sqrt{c_{3}^{2}-8}+c_{3}}{2}\text{, }|c_{3}|\geq 2\sqrt{2}$$