Answer:
[tex]x=\frac{-y+\sqrt{y^2+4rt} }{2r}[/tex]
[tex]x=\frac{-y-\sqrt{y^2+4rt} }{2r}[/tex]
Explanation:
[tex]rx+y=\frac{t}{x}\\\\x(rx+y)=(\frac{t}{x})x\\\\rx^2+yx=t\\\\rx^2+yx-t=t-t\\\\rx^2+yx-t=0[/tex]
Solve using the quadratic formula.
[tex]x=\frac{-y+\sqrt{y^2+4rt} }{2r}[/tex]
[tex]x=\frac{-y-\sqrt{y^2+4rt} }{2r}[/tex]
