#### Answer

$\frac{-5\pm\sqrt{13}}{2}$

#### Work Step by Step

We solve using the quadratic formula:
$3+5z+z^{2}=0$
$z^{2}+5z+3=0$
$z=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}=\frac{-(5)\pm\sqrt{(5)^{2}-4(1)(3)}}{2(1)}=\frac{-5\pm\sqrt{25-12}}{2}=\frac{-5\pm\sqrt{13}}{2}$