Solve xθ-x^2=θ

$$x \theta - { x }^{ 2 } = \theta$$

Solve for θ

$$\theta =\frac{x^{2}}{x-1}$$

$$x\neq 1$$

Steps for Solving Linear Equation

Subtract \theta from both sides.

$$x\theta -x^{2}-\theta =0$$

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

$$x\theta -\theta =x^{2}$$

Combine all terms containing \theta .

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

Divide both sides by x-1.

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

Dividing by x-1 undoes the multiplication by x-1.

$$\theta =\frac{x^{2}}{x-1}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{\theta \left(\theta -4\right)}+\theta }{2}$$

$$x=\frac{\sqrt{\theta \left(\theta -4\right)}+\theta }{2}$$

Solve for x

$$x=\frac{-\sqrt{\theta \left(\theta -4\right)}+\theta }{2}$$

$$x=\frac{\sqrt{\theta \left(\theta -4\right)}+\theta }{2}\text{, }\theta \geq 4\text{ or }\theta \leq 0$$