[tex]x+y=5\\
xy=-180\\\\
x=5-y\\
xy=-180\\\\
(5-y)y=-180\\
5y-y^2+180=0\\
-y^2+5y+180=0\\
\Delta=5^2-4\cdot(-1)\cdot180=25+720=745\\
\sqrt{\Delta}=\sqrt{745}\\
y_1=\dfrac{-5-\sqrt{745}}{2\cdot(-1)}=\dfrac{5+\sqrt{745}}{2}\\
y_2=\dfrac{-5+\sqrt{745}}{2\cdot(-1)}=\dfrac{5-\sqrt{745}}{2}\\\\
x_1=5-\dfrac{5+\sqrt{745}}{2}=\dfrac{10}{2}-\dfrac{5+\sqrt{745}}{2}=\dfrac{5-\sqrt{745}}{2}\\
x_2=5-\dfrac{5-\sqrt{745}}{2}=\dfrac{10}{2}-\dfrac{5-\sqrt{745}}{2}=\dfrac{5+\sqrt{745}}{2}[/tex]
These numbers are [tex]\dfrac{5+\sqrt{745}}{2}[/tex] and [tex]\dfrac{5-\sqrt{745}}{2}[/tex].
