Resposta:

[tex]x_{1} = -12-2\sqrt{39}[/tex] e [tex]x_{2} = -12+2\sqrt{39}[/tex]

Explicação passo a passo:

[tex]\begin{aligned}\frac{2x-3}{x+6} = \frac{3x-1}{x-2} & \iff (2x-3)(x-2) = (3x-1)(x+6)\\& \iff x^{2}+24x-12 = 0 \iff x_{1,2} = \frac{-24\pm\sqrt{24^{2}-4(1)(-12)}}{2}\\& \iff x_{1,2} = \frac{-24\pm \sqrt{624}}{2} \iff x_{1,2} = \frac{-24\pm 4\sqrt{29}}{2} \\& \iff x_{1,2} = \frac{-12\pm2\sqrt{39}}{2} \iff \begin{cases} x_{1} = \frac{-12 - 2\sqrt{39}}{2} \\ x_{2} = \frac{-12 + 2\sqrt{39}}{2} \end{cases}\end{aligned}[/tex]