The equation shown in the image is:

$x^2 + 6x + 5 = 0$

with the coefficients identified as $a = 1$, $b = 6$, and $c = 5$.

This is a quadratic equation, and to solve it, we can use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Substituting the values of $a$, $b$, and $c$ into the formula:

$x = \frac{-6 \pm \sqrt{6^2 - 4(1)(5)}}{2(1)}$ $x = \frac{-6 \pm \sqrt{36 - 20}}{2}$ $x = \frac{-6 \pm \sqrt{16}}{2}$ $x = \frac{-6 \pm 4}{2}$

This gives two possible solutions:

$x_1 = \frac{-6 + 4}{2} = \frac{-2}{2} = -1$ $x_2 = \frac{-6 - 4}{2} = \frac{-10}{2} = -5$

Thus, the solutions are:

$x_1 = -1, \quad x_2 = -5$

Would you like a deeper explanation or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you determine when a quadratic equation has real or complex solutions?
2. Can you solve a quadratic equation by factoring, and how does it compare to using the quadratic formula?
3. How do the values of $a$, $b$, and $c$ in a quadratic equation influence the shape of its graph?
4. What is the discriminant of a quadratic equation, and what does it tell you about the solutions?
5. How can you complete the square to solve a quadratic equation?

Tip: Always check the discriminant $b^2 - 4ac$ before solving. If it's positive, you will have two real solutions, if zero, one real solution, and if negative, complex solutions.