Solve 3x^2-3x-2k=0

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

Solve for k

$$k=\frac{3x\left(x-1\right)}{2}$$

Steps for Solving Linear Equation

Subtract 3x^{2} from both sides. Anything subtracted from zero gives its negation.

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

Add 3x to both sides.

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

The equation is in standard form.

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

Divide both sides by -2.

$$\frac{-2k}{-2}=\frac{3x\left(1-x\right)}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$k=\frac{3x\left(1-x\right)}{-2}$$

Divide 3x\left(1-x\right) by -2.

$$k=-\frac{3x\left(1-x\right)}{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{24k+9}}{6}+\frac{1}{2}$$

$$x=-\frac{\sqrt{24k+9}}{6}+\frac{1}{2}$$

Solve for x

$$x=\frac{\sqrt{24k+9}}{6}+\frac{1}{2}$$

$$x=-\frac{\sqrt{24k+9}}{6}+\frac{1}{2}\text{, }k\geq -\frac{3}{8}$$