Answer
$$-0.8 + 0.4j, \ or, \ -0.8 -0.4j
.$$
Work Step by Step
For the equation $5x^2 +8x+4= 0$, we use the quadratic formula as follows
$$
x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a},
\\
a=5, \quad b=8, \quad c=4
.$$
That is,
$$
x=\frac{-8\pm \sqrt{64-80}}{2(5) }=-0.8 + 0.4j, \ or, \ -0.8 -0.4j
.$$
