Chapter 1, Equations and Graphs - Section 1.4 - Solving Quadratic Equations - 1.4 Exercises - Page 123: 42

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

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