Solve x^2-kx+3k=0

$$x ^ { 2 } - k x + 3 k = 0$$

Solve for k

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

$$x\neq 3$$

Steps for Solving Linear Equation

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

$$-kx+3k=-x^{2}$$

Combine all terms containing k.

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

The equation is in standard form.

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

Divide both sides by -x+3.

$$\frac{\left(3-x\right)k}{3-x}=-\frac{x^{2}}{3-x}$$

Dividing by -x+3 undoes the multiplication by -x+3.

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

Solve for x (complex solution)

$$x=\frac{\sqrt{k\left(k-12\right)}+k}{2}$$

$$x=\frac{-\sqrt{k\left(k-12\right)}+k}{2}$$

Solve for x

$$x=\frac{\sqrt{k\left(k-12\right)}+k}{2}$$

$$x=\frac{-\sqrt{k\left(k-12\right)}+k}{2}\text{, }k\geq 12\text{ or }k\leq 0$$