It looks like you are working with a polynomial equation in terms of \( z \):

\[
2yz^2 - 4y^2z + 5yz - A = 0
\]

This is a quadratic equation in the variable \( z \). The general form of a quadratic equation is:

\[
az^2 + bz + c = 0
\]

where:

- \( a = 2y \)
- \( b = -4y^2 + 5y \)
- \( c = -A \)

If you are looking to solve this equation for \( z \), you can use the quadratic formula:

\[
z = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Substituting the values for \( a \), \( b \), and \( c \):

\[
z = \frac{-(-4y^2 + 5y) \pm \sqrt{(-4y^2 + 5y)^2 - 4(2y)(-A)}}{2(2y)}
\]

This simplifies to:

\[
z = \frac{4y^2 - 5y \pm \sqrt{(4y^2 - 5y)^2 + 8Ay}}{4y}
\]

You can further simplify this expression depending on the specific values of \( A \) and \( y \), or check for specific conditions such as the discriminant \( (b^2 - 4ac) \) being non-negative for real solutions.

If you have more specific details or a particular question regarding this equation, feel free to share!