Given:
[tex]\frac{2}{x-5}=\frac{x-4}{6}[/tex]
Required:
To find the value of x.
Explanation:
Consider the given equation,
[tex]\frac{2}{x-5}=\frac{x-4}{6}[/tex][tex]\begin{gathered} (x-5)(x-4)=12 \\ x^2-5x-4x+20=12 \\ x^2-9x+20=12 \\ x^2-9x+8=0 \end{gathered}[/tex]
Now, the value of x is
[tex]\begin{gathered} x=\frac{-9\pm\sqrt{81-32}}{2} \\ =\frac{-9\pm\sqrt{49}}{2} \\ =\frac{-9\pm7}{2} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{-9+7}{2} \\ =\frac{-2}{2} \\ =-1 \end{gathered}[/tex]
OR
[tex]\begin{gathered} x=\frac{-9-7}{2} \\ =-\frac{16}{2} \\ =-8 \end{gathered}[/tex]
Final Answer:
The values of x are
[tex]x=-1,-8[/tex]
