[tex]6r^2-10r-24 =0\\ \\a=6, \ b= -10, \ c= -24 \\ \\ \Delta =b^2-4ac = (-10)^2 -4\cdot6\cdot (-24) = 100+576 = 676 \\ \\ r_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{10-\sqrt{676}}{2\cdot 6 }=\frac{ 10-26}{12}= \frac{-16}{12}=- \frac{4}{3} \\ \\r_{2}=\frac{-b+\sqrt{\Delta }}{2a}= \frac{10+\sqrt{676}}{2\cdot 6 }=\frac{ 10+26}{12}= \frac{36}{12}=3\\ \\ 6r^2-10r-24 = 6(r+\frac{4}{3})(r-3)=(6r+8)(r-3)\\ \\ \\ Answer : \ 6r^2-10r-24 =(6r-8)(r-3)[/tex]
