Solve np+n(n+1)/2=7224

$$n p + \frac { n ( n + 1 ) } { 2 } = 7224$$

Solve for p

$$p=-\frac{n}{2}-\frac{1}{2}+\frac{7224}{n}$$

$$n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2np+n\left(n+1\right)=14448$$

Use the distributive property to multiply n by n+1.

$$2np+n^{2}+n=14448$$

Subtract n^{2} from both sides.

$$2np+n=14448-n^{2}$$

Subtract n from both sides.

$$2np=14448-n^{2}-n$$

The equation is in standard form.

$$2np=14448-n-n^{2}$$

Divide both sides by 2n.

$$\frac{2np}{2n}=\frac{14448-n-n^{2}}{2n}$$

Dividing by 2n undoes the multiplication by 2n.

$$p=\frac{14448-n-n^{2}}{2n}$$

Divide 14448-n^{2}-n by 2n.

$$p=-\frac{n}{2}-\frac{1}{2}+\frac{7224}{n}$$

Solve for n

$$n=\frac{\sqrt{4p^{2}+4p+57793}}{2}-p-\frac{1}{2}$$

$$n=-\frac{\sqrt{4p^{2}+4p+57793}}{2}-p-\frac{1}{2}$$