[tex]45=x(14-x)\\\\45=x\cdot14-x\cdot x\\\\45=14x-x^2\\\\-x^2+14x-45=0\\\\a=-1;\ b=14;\ c=-45\\\\\Delta=b^2-4ac;\ \Delta=14^2-4\cdot(-1)\cdot(-45)=196-180=16\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\x_1=\frac{-14-\sqrt{16}}{2\cdot(-1)}=\frac{-14-4}{-2}=\frac{-18}{-2}=9\\\\x_2=\frac{-14+\sqrt{16}}{2\cdot(-1)}=\frac{-14+4}{-2}=\frac{-10}{-2}=5[/tex]
[tex]Answer:x=9\ or\ x=5.[/tex]
