Solve x^2-2kx-6=0

$$x ^ { 2 } - 2 k x - 6 = 0$$

Solve for k

$$k=\frac{x}{2}-\frac{3}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$-2kx-6=-x^{2}$$

Add 6 to both sides.

$$-2kx=-x^{2}+6$$

The equation is in standard form.

$$\left(-2x\right)k=6-x^{2}$$

Divide both sides by -2x.

$$\frac{\left(-2x\right)k}{-2x}=\frac{6-x^{2}}{-2x}$$

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

$$k=\frac{6-x^{2}}{-2x}$$

Divide -x^{2}+6 by -2x.

$$k=\frac{x}{2}-\frac{3}{x}$$

Solve for x

$$x=\sqrt{k^{2}+6}+k$$

$$x=-\sqrt{k^{2}+6}+k$$