Answer
$\frac{8\pm\sqrt{14}}{10}$
Work Step by Step
We use the quadratic formula:
$10y^{2}-16y+5=0$
$x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}=\frac{-(-16)\pm\sqrt{(-16)^{2}-4(10)(5)}}{2(10)}=\frac{16\pm\sqrt{256-200}}{20}=\frac{16\pm\sqrt{56}}{20}=\frac{16\pm\sqrt{4*14}}{20}=\frac{16\pm2\sqrt{14}}{20}=\frac{8\pm\sqrt{14}}{10}$