Use the square roots property to solve the quadratic equation \( \left(9 z+\frac{1}{2}\right)^{2}+61=39 \). If there are multiple answer them separated by a comma, e.g. 1,2 . If there is no real solution, enter \( \varnothing \). Provide your answer below:

To solve the quadratic equation \( \left(9 z+\frac{1}{2}\right)^{2}+61=39 \), let's first isolate the squared term: \[ \left(9 z+\frac{1}{2}\right)^{2} = 39 - 61 \] This simplifies to: \[ \left(9 z+\frac{1}{2}\right)^{2} = -22 \] Since the square of a real number cannot equal a negative value, there are no real solutions. Thus, we write: \[ \varnothing \]