To find the value of the discriminant for the quadratic equation \(4n^2 = 5n + 8\), we first need to rearrange the equation into the standard quadratic form, which is \(ax^2 + bx + c = 0\).
Starting with the given equation:
\[ 4n^2 - 5n - 8 = 0 \]
Here, the coefficients are:
- \(a = 4\)
- \(b = -5\)
- \(c = -8\)
The discriminant \(D\) is calculated using the formula:
\[ D = b^2 - 4ac \]
Substituting the values of \(a\), \(b\), and \(c\):
\[ D = (-5)^2 - 4(4)(-8) \] \[ D = 25 - 4(4)(-8) \] \[ D = 25 - (-128) \] \[ D = 25 + 128 \] \[ D = 153 \]
Thus, the value of the discriminant for the quadratic equation \(4n^2 = 5n + 8\) is \(\boxed{153}\).