4. Given complex numbers $z_{1}, z_{2}$ satisfy $\left|z_{1}\right|=1,\left|z_{2}\right|=\frac{5}{2},\left|3 z_{1}-2 z_{2}\right|=7$, then $\frac{z_{1}}{z_{2}}=$
4. $-\frac{1}{5}(1 \pm \sqrt{3} \mathrm{i})$.

From the given, we have $z_{1} \overline{z_{1}}=1, z_{2} \overline{z_{2}}=\frac{25}{4}$,
$$
\left(3 z_{1}-2 z_{2}\right)\left(3 \overline{z_{1}}-2 \overline{z_{2}}\right)=49 \Rightarrow 9 z_{1} \overline{z_{1}}+4 z_{2} \overline{z_{2}}-6\left(z_{1} \overline{z_{2}}+\overline{z_{1}} z_{2}\right)=49,
$$

then
$$
z_{1} \overline{z_{2}}+\overline{z_{1}} z_{2}=-\frac{5}{2} \Rightarrow \frac{z_{1}}{z_{2}} \cdot \frac{25}{4}+\frac{z_{2}}{z_{1}}=-\frac{5}{2} .
$$

Let $t=\frac{z_{1}}{z_{2}}$, then $\frac{25}{4} t+\frac{1}{t}=-\frac{5}{2}$. Solving for $t$ yields $t=-\frac{1}{5}(1 \pm \sqrt{3} \mathrm{i})$.