Solve x^2-2kx+5k-6=0

$$x ^ { 2 } - 2 k x + 5 k - 6 = 0$$

Solve for k

$$k=-\frac{x^{2}-6}{5-2x}$$

$$x\neq \frac{5}{2}$$

Steps for Solving Linear Equation

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

$$-2kx+5k-6=-x^{2}$$

Add 6 to both sides.

$$-2kx+5k=-x^{2}+6$$

Combine all terms containing k.

$$\left(-2x+5\right)k=-x^{2}+6$$

The equation is in standard form.

$$\left(5-2x\right)k=6-x^{2}$$

Divide both sides by -2x+5.

$$\frac{\left(5-2x\right)k}{5-2x}=\frac{6-x^{2}}{5-2x}$$

Dividing by -2x+5 undoes the multiplication by -2x+5.

$$k=\frac{6-x^{2}}{5-2x}$$

Solve for x (complex solution)

$$x=\sqrt{\left(k-3\right)\left(k-2\right)}+k$$

$$x=-\sqrt{\left(k-3\right)\left(k-2\right)}+k$$

Solve for x

$$x=\sqrt{\left(k-3\right)\left(k-2\right)}+k$$

$$x=-\sqrt{\left(k-3\right)\left(k-2\right)}+k\text{, }k\leq 2\text{ or }k\geq 3$$