$y^2-5y+\dfrac{5}{2}$
$=y^2-2y.\dfrac{5}{2}+\dfrac{25}{4}-\dfrac{15}{4}$
$=\Big(y-\dfrac{5}{2}\Big)^2-\dfrac{15}{4}$
$=\Big(y-\dfrac{5}{2}\Big)^2-\Big(\dfrac{\sqrt{15}}{2}\Big)^2$
$=\Big(y-\dfrac{5}{2}-\dfrac{\sqrt{15}}{2}\Big).\Big(y-\dfrac{5}{2}+\dfrac{\sqrt{15}}{2}\Big)$
$=\Big(y-\dfrac{5+\sqrt{15}}{2}\Big).\Big(y-\dfrac{5-\sqrt{15}}{2}\Big)$