Solve 2x^2+6x+9=cx

$$2 x ^ { 2 } + 6 x + 9 = c x$$

Solve for c

$$c=2x+6+\frac{9}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$cx=2x^{2}+6x+9$$

The equation is in standard form.

$$xc=2x^{2}+6x+9$$

Divide both sides by x.

$$\frac{xc}{x}=\frac{2x^{2}+6x+9}{x}$$

Dividing by x undoes the multiplication by x.

$$c=\frac{2x^{2}+6x+9}{x}$$

Divide 2x^{2}+6x+9 by x.

$$c=2x+6+\frac{9}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{c^{2}-12c-36}+c-6}{4}$$

$$x=\frac{-\sqrt{c^{2}-12c-36}+c-6}{4}$$

Solve for x

$$x=\frac{\sqrt{c^{2}-12c-36}+c-6}{4}$$

$$x=\frac{-\sqrt{c^{2}-12c-36}+c-6}{4}\text{, }c\geq 6\sqrt{2}+6\text{ or }c\leq 6-6\sqrt{2}$$