Solve the equation $20 z^{2}+3 z-9=0$. Answer: $z=$ Write your answers as a list of integers or reduced fractions, with your answers separated by (a) comma(s). For example, if you get 4 and $-\frac{2}{3}$ as your answers, then enter $4,-2 / 3$ in the box.

Step 1 ：The given equation is a quadratic equation in the form of \(ax^2 + bx + c = 0\). We can solve it using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).

Step 2 ：Here, \(a = 20\), \(b = 3\), and \(c = -9\).

Step 3 ：Substituting these values into the quadratic formula, we get:

Step 4 ：\(z = \frac{-3 \pm \sqrt{3^2 - 4*20*(-9)}}{2*20}\)

Step 5 ：\(z = \frac{-3 \pm \sqrt{9 + 720}}{40}\)

Step 6 ：\(z = \frac{-3 \pm \sqrt{729}}{40}\)

Step 7 ：\(z = \frac{-3 \pm 27}{40}\)

Step 8 ：So, the solutions are:

Step 9 ：\(z = \frac{-3 + 27}{40} = \frac{24}{40} = \frac{3}{5}\)

Step 10 ：and

Step 11 ：\(z = \frac{-3 - 27}{40} = \frac{-30}{40} = -\frac{3}{4}\)

Step 12 ：Thus, the solutions to the equation are \(\boxed{\frac{3}{5}, -\frac{3}{4}}\).