Solve 6H+(n-1)*2/2*n=858

$$\frac { 6 H + ( n - 1 ) \cdot 2 } { 2 } \cdot n = 858$$

Solve for H

$$H=-\frac{n}{3}+\frac{1}{3}+\frac{286}{n}$$

$$n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$\left(6H+\left(n-1\right)\times 2\right)n=1716$$

Use the distributive property to multiply n-1 by 2.

$$\left(6H+2n-2\right)n=1716$$

Use the distributive property to multiply 6H+2n-2 by n.

$$6Hn+2n^{2}-2n=1716$$

Subtract 2n^{2} from both sides.

$$6Hn-2n=1716-2n^{2}$$

Add 2n to both sides.

$$6Hn=1716-2n^{2}+2n$$

The equation is in standard form.

$$6nH=1716+2n-2n^{2}$$

Divide both sides by 6n.

$$\frac{6nH}{6n}=\frac{1716+2n-2n^{2}}{6n}$$

Dividing by 6n undoes the multiplication by 6n.

$$H=\frac{1716+2n-2n^{2}}{6n}$$

Divide 1716-2n^{2}+2n by 6n.

$$H=-\frac{n}{3}+\frac{1}{3}+\frac{286}{n}$$

Solve for n

$$n=\frac{\sqrt{9H^{2}-6H+3433}-3H+1}{2}$$

$$n=\frac{-\sqrt{9H^{2}-6H+3433}-3H+1}{2}$$