[tex]\\ \tt\longmapsto \dfrac{9}{x+2}=\dfrac{x+3}{x-5}[/tex]
[tex]\\ \tt\longmapsto 9(x-5)=(x+2)(x+3)[/tex]
[tex]\\ \tt\longmapsto 9x-45=x^2+5x+6[/tex]
[tex]\\ \tt\longmapsto x^2-4x+51=0[/tex]
Let's find x
[tex]\\ \tt\hookrightarrow x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\\ \tt\hookrightarrow x=\dfrac{4\pm\sqrt{16-204}}{2}[/tex]
[tex]\\ \tt\hookrightarrow x=\dfrac{4\pm \sqrt{-188}}{2}[/tex]
[tex]\\ \tt\hookrightarrow x=\dfrac{4\pm \sqrt{188}i}{2}[/tex]
[tex]\\ \tt\hookrightarrow x=\dfrac{4\pm 2\sqrt{47}i}{2}[/tex]
[tex]\\ \tt\hookrightarrow x=2\pm \sqrt{47}i[/tex]
