The equation in the image is:

$2x - x^2 = 1$

This is a quadratic equation. To solve it, we can rearrange it into the standard form $ax^2 + bx + c = 0$.

Steps to solve:

1. Rearrange the equation: $-x^2 + 2x - 1 = 0$ Multiply the entire equation by $-1$ to simplify: $x^2 - 2x + 1 = 0$

2. Now we have the equation $x^2 - 2x + 1 = 0$. This can be factored as: $(x - 1)^2 = 0$

3. Solve for $x$: $x - 1 = 0$ $x = 1$

Thus, the solution is $x = 1$.

Would you like further details or have any questions?

Here are five related questions you could explore:

1. How do you solve quadratic equations using the quadratic formula?
2. What are the different methods of solving quadratic equations (e.g., completing the square)?
3. What are the characteristics of a quadratic equation with a double root?
4. How do you graph quadratic functions, and what does the vertex represent?
5. Can quadratic equations always be factored, and what if they cannot?

Tip: Always check if a quadratic can be factored easily before using other methods like the quadratic formula.