Answer
$0, \ or, \ -\frac{2}{5}$
Work Step by Step
For the equation $5x^2 +2x = 0$, we use the quadratic formula as follows
$$
x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a},
\\
a=5, \quad b=2, \quad c=0
.$$
That is, $$ x=\frac{-2 \pm \sqrt{4+0}}{10 }=\frac{-2\pm2}{10 }=0, \ or, \ -\frac{2}{5}
.$$
Check the result:
$$
5(0^2)+5(0)=0+0=0, \quad
5((2/5)^2)-2(2/5)=(4/5)-(4/5)=0.
$$
