Solve 2x=n^2+n

$$2 x = n ^ { 2 } + n$$

Solve for x

$$x=\frac{n\left(n+1\right)}{2}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$2x=n^{2}+n$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{n\left(n+1\right)}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{n\left(n+1\right)}{2}$$

Solve for n (complex solution)

$$n=\frac{-\sqrt{8x+1}-1}{2}$$

$$n=\frac{\sqrt{8x+1}-1}{2}$$

Solve for n

$$n=\frac{-\sqrt{8x+1}-1}{2}$$

$$n=\frac{\sqrt{8x+1}-1}{2}\text{, }x\geq -\frac{1}{8}$$