Solve z^2-2az+3=0

$$z ^ { 2 } - 2 a z + 3 = 0$$

Solve for a

$$a=\frac{z}{2}+\frac{3}{2z}$$

$$z\neq 0$$

Steps for Solving Linear Equation

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

$$-2az+3=-z^{2}$$

Subtract 3 from both sides.

$$-2az=-z^{2}-3$$

The equation is in standard form.

$$\left(-2z\right)a=-z^{2}-3$$

Divide both sides by -2z.

$$\frac{\left(-2z\right)a}{-2z}=\frac{-z^{2}-3}{-2z}$$

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

$$a=\frac{-z^{2}-3}{-2z}$$

Divide -z^{2}-3 by -2z.

$$a=\frac{z}{2}+\frac{3}{2z}$$

Solve for z (complex solution)

$$z=\sqrt{a^{2}-3}+a$$

$$z=-\sqrt{a^{2}-3}+a$$

Solve for z

$$z=\sqrt{a^{2}-3}+a$$

$$z=-\sqrt{a^{2}-3}+a\text{, }|a|\geq \sqrt{3}$$