Solve 3x^2-3x+m=0

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

Solve for m

$$m=-3x\left(x-1\right)$$

Solution Steps

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

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

Add 3x to both sides.

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

Solve for x (complex solution)

$$x=\frac{\sqrt{9-12m}}{6}+\frac{1}{2}$$

$$x=-\frac{\sqrt{9-12m}}{6}+\frac{1}{2}$$

Solve for x

$$x=\frac{\sqrt{9-12m}}{6}+\frac{1}{2}$$

$$x=-\frac{\sqrt{9-12m}}{6}+\frac{1}{2}\text{, }m\leq \frac{3}{4}$$