Problem 5. (20 points) A point is randomly thrown onto the segment $[6 ; 10]$ and let $k-$ be the obtained value. Find the probability that the roots of the equation $\left(k^{2}-3 k-10\right) x^{2}+(3 k-8) x+2=0$ satisfy the condition $x_{1} \leq 2 x_{2}$.