The equation in the image appears to be a quadratic equation being solved using the quadratic formula:

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

From the image:

$x = \frac{-5 \pm \sqrt{5^2 - 4 \cdot 1 \cdot 4}}{2}$

Step-by-step solution:

1. Calculate $b^2$: $5^2 = 25$

2. Calculate the discriminant ($b^2 - 4ac$): $25 - 4 \cdot 1 \cdot 4 = 25 - 16 = 9$

3. Substitute the discriminant into the formula: $x = \frac{-5 \pm \sqrt{9}}{2}$

4. Simplify $\sqrt{9}$: $\sqrt{9} = 3$

5. Write the two possible solutions: $x_1 = \frac{-5 + 3}{2} = \frac{-2}{2} = -1$ $x_2 = \frac{-5 - 3}{2} = \frac{-8}{2} = -4$

Final Answer:

The solutions are: $x = -1 \quad \text{and} \quad x = -4$

Would you like further clarification or a detailed explanation of any step? Let me know! Here are some related questions you might explore:

1. How is the discriminant used to determine the nature of the roots?
2. What happens when the discriminant is negative?
3. How do we solve quadratic equations by factoring?
4. Can you derive the quadratic formula from the standard equation $ax^2 + bx + c = 0$?
5. How can quadratic equations be applied in real-life scenarios?

Tip: Always check the discriminant first to see if the roots are real, imaginary, or repeated!