Solve frac{sqrt{3}}{3}x+m=x^2+frac{sqrt{3}}{3}x

$$\frac { \sqrt { 3 } } { 3 } x + m = x ^ { 2 } + \frac { \sqrt { 3 } } { 3 } x$$

Solve for m

$$m=x^{2}$$

Solution Steps

Multiply both sides of the equation by 3.

$$\sqrt{3}x+3m=3x^{2}+\sqrt{3}x$$

Subtract \sqrt{3}x from both sides.

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

Combine \sqrt{3}x and -\sqrt{3}x to get 0.

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

Cancel out 3 on both sides.

$$m=x^{2}$$

Solve for x (complex solution)

$$x=-\sqrt{m}$$

$$x=\sqrt{m}$$

Solve for x

$$x=\sqrt{m}$$

$$x=-\sqrt{m}\text{, }m\geq 0$$