Answer
$\displaystyle -\frac{3}{10}\pm\frac{1}{10}i$
Work Step by Step
$10x^{2}+6x+1=0$
We solve using the quadratic formula ($a=10,\ b=6,\ c=1$):
$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$\displaystyle x=\frac{-6\pm\sqrt{6^{2}-4(10)(1)}}{2(10)}$
$\displaystyle x=\frac{-6\pm\sqrt{36-40}}{2(10)}$
$\displaystyle x=\frac{-6\pm\sqrt{-4}}{20}$
$\displaystyle x=\frac{-6\pm 2i}{20}=-\frac{3}{10}\pm\frac{1}{10}i$
Recall, $i=\sqrt{-1}$
