Solve x+a=2x-5/a

$$x + a = \frac { 2 x - 5 } { a }$$

Solve for x

$$x=-\frac{a^{2}+5}{a-2}$$

$$a\neq 2\text{ and }a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$ax+aa=2x-5$$

Multiply a and a to get a^{2}.

$$ax+a^{2}=2x-5$$

Subtract 2x from both sides.

$$ax+a^{2}-2x=-5$$

Subtract a^{2} from both sides.

$$ax-2x=-5-a^{2}$$

Combine all terms containing x.

$$\left(a-2\right)x=-5-a^{2}$$

The equation is in standard form.

$$\left(a-2\right)x=-a^{2}-5$$

Divide both sides by a-2.

$$\frac{\left(a-2\right)x}{a-2}=\frac{-a^{2}-5}{a-2}$$

Dividing by a-2 undoes the multiplication by a-2.

$$x=\frac{-a^{2}-5}{a-2}$$

Divide -5-a^{2} by a-2.

$$x=-\frac{a^{2}+5}{a-2}$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=\frac{-\sqrt{\left(x-2\right)\left(x+10\right)}-x}{2}\text{, }&\text{unconditionally}\\a=\frac{\sqrt{\left(x-2\right)\left(x+10\right)}-x}{2}\text{, }&x\neq \frac{5}{2}\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}a=\frac{-\sqrt{\left(x-2\right)\left(x+10\right)}-x}{2}\text{, }&x\leq -10\text{ or }x\geq 2\\a=\frac{\sqrt{\left(x-2\right)\left(x+10\right)}-x}{2}\text{, }&x\leq -10\text{ or }\left(x\neq \frac{5}{2}\text{ and }x\geq 2\right)\end{matrix}\right.$$