Let the number be x.
[tex]\frac{1}{2}(x+4)=\frac{5}{x}-3\\\\x+4=\frac{10}{x}-6\\\\x+10=\frac{10}{x}\\\\x^2-\frac{10}{x}+10=0\\\\\frac{x^2+10x-10}{x}=0\\\\ x\neq0\\\\x^2+10x-10=0\\\\ x=\frac{-10\pm \sqrt{10^2-4 \times (-10)}}{2\times 1}\\\\x=\frac{-10 \pm \sqrt{140}}{2}[/tex]
For a Quadratic equation of the form
Ax²+Bx+c=0
D=B²-4AC
[tex]x=\frac{-B \pm \sqrt{D}}{2A}[/tex]
