Solve x^2-2lambdax+lambda=0

$$x ^ { 2 } - 2 \lambda x + \lambda = 0$$

Solve for λ

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

$$x\neq \frac{1}{2}$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-2\lambda x+\lambda =-x^{2}$$

Combine all terms containing \lambda .

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

The equation is in standard form.

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

Divide both sides by -2x+1.

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

Dividing by -2x+1 undoes the multiplication by -2x+1.

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

Solve for x (complex solution)

$$x=\sqrt{\lambda \left(\lambda -1\right)}+\lambda$$

$$x=-\sqrt{\lambda \left(\lambda -1\right)}+\lambda$$

Solve for x

$$x=\sqrt{\lambda \left(\lambda -1\right)}+\lambda$$

$$x=-\sqrt{\lambda \left(\lambda -1\right)}+\lambda \text{, }\lambda \geq 1\text{ or }\lambda \leq 0$$