To turn the fractions $-\frac{2}{3}$ and $\frac{3}{4}$ into a quadratic equation, we need to use these values as the roots of the quadratic equation. If $x_1$ and $x_2$ are the roots, then the quadratic equation can be written as:

$(x - x_1)(x - x_2) = 0$

Substituting the roots:

$(x + \frac{2}{3})(x - \frac{3}{4}) = 0$

Now, let's simplify this equation.

First, expand the expression:

$x^2 - \frac{3}{4}x + \frac{2}{3}x - \frac{2}{3} \times \frac{3}{4} = 0$

Next, combine like terms and simplify:

$x^2 + \left(\frac{2}{3} - \frac{3}{4}\right)x - \frac{6}{12} = 0$

Simplifying further:

$x^2 - \frac{1}{12}x - \frac{1}{2} = 0$

The quadratic equation that has $-\frac{2}{3}$ and $\frac{3}{4}$ as roots is:

$x^2 - \frac{1}{12}x - \frac{1}{2} = 0$

Do you want more details or have any questions?

Here are five related questions to expand your understanding:

1. How do you find the sum of the roots of a quadratic equation?
2. What is the significance of the discriminant in a quadratic equation?
3. How can you factorize a quadratic equation?
4. How do you complete the square to solve a quadratic equation?
5. What are the real-world applications of quadratic equations?

Tip: When dealing with fractions in quadratic equations, it's helpful to first clear the fractions by multiplying through by the least common denominator.