Solve 3x^2+2n-1=0

$$3 x ^ { 2 } + 2 n - 1 = 0$$

Solve for n

$$n=\frac{1-3x^{2}}{2}$$

Steps for Solving Linear Equation

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

$$2n-1=-3x^{2}$$

Add 1 to both sides.

$$2n=-3x^{2}+1$$

The equation is in standard form.

$$2n=1-3x^{2}$$

Divide both sides by 2.

$$\frac{2n}{2}=\frac{1-3x^{2}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$n=\frac{1-3x^{2}}{2}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{3-6n}}{3}$$

$$x=\frac{\sqrt{3-6n}}{3}$$

Solve for x

$$x=\frac{\sqrt{3-6n}}{3}$$

$$x=-\frac{\sqrt{3-6n}}{3}\text{, }n\leq \frac{1}{2}$$