Solve (c)x^2-3x-9=0

$$( c ) x ^ { 2 } - 3 x - 9 = 0$$

Solve for c

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

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$cx^{2}-9=3x$$

Add 9 to both sides.

$$cx^{2}=3x+9$$

The equation is in standard form.

$$x^{2}c=3x+9$$

Divide both sides by x^{2}.

$$\frac{x^{2}c}{x^{2}}=\frac{3x+9}{x^{2}}$$

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

$$c=\frac{3x+9}{x^{2}}$$

Divide 9+3x by x^{2}.

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{3\left(\sqrt{4c+1}+1\right)}{2c}\text{; }x=\frac{3\left(-\sqrt{4c+1}+1\right)}{2c}\text{, }&c\neq 0\\x=-3\text{, }&c=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{3\left(\sqrt{4c+1}+1\right)}{2c}\text{; }x=\frac{3\left(-\sqrt{4c+1}+1\right)}{2c}\text{, }&c\neq 0\text{ and }c\geq -\frac{1}{4}\\x=-3\text{, }&c=0\end{matrix}\right.$$