Answer
$-0.2 + 0.748j, \ or, \ -0.2 - 0.748j$
Work Step by Step
For the equation $5x^2 +2x+3= 0$, we use the quadratic formula as follows
$$
x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a},
\\
a=5, \quad b=2, \quad c=3
.$$
That is,
$$
x=\frac{-2\pm \sqrt{4-60}}{2(5) }=-0.2 + 0.748j, \ or, \ -0.2 - 0.748j
.$$
