Solve x=n(3n-1)/2

$$x = n ( 3 n - 1 ) / 2$$

Solve for x

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

Solution Steps

Use the distributive property to multiply n by 3n-1.

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

Divide each term of 3n^{2}-n by 2 to get \frac{3}{2}n^{2}-\frac{1}{2}n.

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

Solve for n (complex solution)

$$n=\frac{\sqrt{24x+1}+1}{6}$$

$$n=\frac{-\sqrt{24x+1}+1}{6}$$

Solve for n

$$n=\frac{\sqrt{24x+1}+1}{6}$$

$$n=\frac{-\sqrt{24x+1}+1}{6}\text{, }x\geq -\frac{1}{24}$$