To solve the equation:

\[
\frac{10 - h}{4 + h} = h
\]

Let's follow these steps:

### Step 1: Eliminate the fraction
Multiply both sides of the equation by \( (4 + h) \) to get rid of the denominator:

\[
10 - h = h(4 + h)
\]

### Step 2: Expand the right side
Expand the right-hand side of the equation:

\[
10 - h = h(4) + h(h) = 4h + h^2
\]

Now we have:

\[
10 - h = 4h + h^2
\]

### Step 3: Rearrange the equation
Move all terms to one side of the equation to set it equal to 0:

\[
0 = h^2 + 4h + h + 10
\]

This simplifies to:

\[
h^2 + 5h - 10 = 0
\]

### Step 4: Solve the quadratic equation
Now we will solve the quadratic equation \( h^2 + 5h - 10 = 0 \) using the quadratic formula:

\[
h = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

For the equation \( h^2 + 5h - 10 = 0 \), we have \( a = 1 \), \( b = 5 \), and \( c = -10 \).

Substitute these values into the quadratic formula:

\[
h = \frac{-5 \pm \sqrt{5^2 - 4(1)(-10)}}{2(1)}
\]

Simplify:

\[
h = \frac{-5 \pm \sqrt{25 + 40}}{2} = \frac{-5 \pm \sqrt{65}}{2}
\]

So the solutions are:

\[
h = \frac{-5 + \sqrt{65}}{2} \quad \text{or} \quad h = \frac{-5 - \sqrt{65}}{2}
\]

### Final Answer:
\[
h = \frac{-5 + \sqrt{65}}{2} \quad \text{or} \quad h = \frac{-5 - \sqrt{65}}{2}
\]

Would you like further details on any step or explanation?

Here are some related questions for you to try:
1. Solve \( \frac{5 - h}{3 + h} = h \).
2. Solve \( \frac{2x - 4}{x + 5} = 3x \).
3. Find the solution to \( 4x^2 + 9x - 2 = 0 \).
4. Solve the equation \( \frac{8 - 2x}{3 + x} = x \).
5. Factor the quadratic equation \( x^2 + 7x + 10 = 0 \).

**Tip:** When solving quadratic equations, you can also try factoring if possible before using the quadratic formula.

Learn how to solve the equation 10 - h = h / (4 + h) using algebraic methods. This guide covers key steps including eliminating the fraction, rearranging terms, and solving the quadratic equation using the quadratic formula. Suitable for students in Grades 8-10.

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