The equation in the image is:

$3x^2 - 3x - 4 = 0$

This is a quadratic equation in the form $ax^2 + bx + c = 0$, where:

• $a = 3$
• $b = -3$
• $c = -4$

We can solve this quadratic equation using the quadratic formula:

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

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

$x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(3)(-4)}}{2(3)}$

Simplifying step by step:

$x = \frac{3 \pm \sqrt{9 + 48}}{6}$ $x = \frac{3 \pm \sqrt{57}}{6}$

So the solutions are:

$x = \frac{3 + \sqrt{57}}{6} \quad \text{or} \quad x = \frac{3 - \sqrt{57}}{6}$

These are the exact solutions to the quadratic equation.

Would you like more details or have any questions about the solution?

Here are some related questions to consider:

1. How would the solution change if the quadratic equation had different coefficients?
2. What is the significance of the discriminant $\sqrt{b^2 - 4ac}$ in the quadratic formula?
3. How can this quadratic equation be factored, if possible?
4. What are the properties of the roots in a quadratic equation with a negative discriminant?
5. How do the roots of this equation relate to the graph of the function $y = 3x^2 - 3x - 4$?

Tip: When solving quadratic equations, always check if the equation can be factored easily before using the quadratic formula. This can sometimes save time!