The image you provided contains seven quadratic equations on a chalkboard. Let's solve each of these one by one.

1) $x^2 - 3x + 4 = 0$

We can solve this quadratic equation using the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ For the equation $x^2 - 3x + 4 = 0$, the coefficients are $a = 1$, $b = -3$, and $c = 4$.

2) $x^2 + 5x + 8 = 0$

Similarly, use the quadratic formula with $a = 1$, $b = 5$, and $c = 8$.

3) $x^2 + 2x = 4$

First, rearrange this equation to standard form: $x^2 + 2x - 4 = 0$ Now apply the quadratic formula with $a = 1$, $b = 2$, and $c = -4$.

4) $4x^2 - 12x + 9 = 0$

Here, the quadratic formula will be used with $a = 4$, $b = -12$, and $c = 9$.

5) $3x^2 + 3x - 4 = 0$

For this equation, the quadratic formula applies with $a = 3$, $b = 3$, and $c = -4$.

6) $2x^2 + 6x - 16 = 4$

Rearrange this equation to standard form: $2x^2 + 6x - 20 = 0$ Now use the quadratic formula with $a = 2$, $b = 6$, and $c = -20$.

7) $5x^2 = 7x + 7$

Rearrange to standard form: $5x^2 - 7x - 7 = 0$ Use the quadratic formula with $a = 5$, $b = -7$, and $c = -7$.

I’ll solve each equation step by step now.Here are the solutions for each quadratic equation:

1. $x^2 - 3x + 4 = 0$: No real solutions (the discriminant is negative).
2. $x^2 + 5x + 8 = 0$: No real solutions (the discriminant is negative).
3. $x^2 + 2x - 4 = 0$: Two real solutions: $x = 1.24$ and $x = -3.24$.
4. $4x^2 - 12x + 9 = 0$: One real solution: $x = 1.5$ (a perfect square).
5. $3x^2 + 3x - 4 = 0$: Two real solutions: $x = 0.76$ and $x = -1.76$.
6. $2x^2 + 6x - 20 = 0$: Two real solutions: $x = 2.0$ and $x = -5.0$.
7. $5x^2 - 7x - 7 = 0$: Two real solutions: $x = 2.07$ and $x = -0.67$.

Would you like more details on any of these solutions or have any questions?

Here are 5 related questions:

1. What is the discriminant, and how does it determine the nature of the solutions?
2. How do you factor quadratic equations when possible?
3. Can every quadratic equation be solved using the quadratic formula?
4. What does it mean when a quadratic equation has no real solutions?
5. How do you graph quadratic equations, and what does the graph tell you about its solutions?

Tip: When the discriminant ($b^2 - 4ac$) is negative, the quadratic equation has no real solutions, only complex ones.