Solve ax^2+4x-a=0

$$a x ^ { 2 } + 4 x - a = 0$$

Solve for a (complex solution)

$$a=-\frac{4x}{x^{2}-1}$$

$$x\neq -1\text{ and }x\neq 1$$

Steps for Solving Linear Equation

Subtract 4x from both sides. Anything subtracted from zero gives its negation.

$$ax^{2}-a=-4x$$

Combine all terms containing a.

$$\left(x^{2}-1\right)a=-4x$$

Divide both sides by x^{2}-1.

$$\frac{\left(x^{2}-1\right)a}{x^{2}-1}=-\frac{4x}{x^{2}-1}$$

Dividing by x^{2}-1 undoes the multiplication by x^{2}-1.

$$a=-\frac{4x}{x^{2}-1}$$

Solve for a

$$a=-\frac{4x}{x^{2}-1}$$

$$|x|\neq 1$$

Steps for Solving Linear Equation

Subtract 4x from both sides. Anything subtracted from zero gives its negation.

$$ax^{2}-a=-4x$$

Combine all terms containing a.

$$\left(x^{2}-1\right)a=-4x$$

Divide both sides by x^{2}-1.

$$\frac{\left(x^{2}-1\right)a}{x^{2}-1}=-\frac{4x}{x^{2}-1}$$

Dividing by x^{2}-1 undoes the multiplication by x^{2}-1.

$$a=-\frac{4x}{x^{2}-1}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{a^{2}+4}-2}{a}\text{; }x=-\frac{\sqrt{a^{2}+4}+2}{a}\text{, }&a\neq 0\\x=0\text{, }&a=0\end{matrix}\right.$$