[tex]24x^2-45x-21=0\\
3(8x^2-15x-7)=0\\
8x^2-15x-7=0\\
\Delta=(-15)^2-4\cdot8\cdot(-7)=225+224=449\\
\sqrt{\Delta}=\sqrt{449}\\
x_1=\dfrac{-(-15)-\sqrt{449}}{2\cdot8}=\dfrac{15-\sqrt{449}}{16}\\
x_2=\dfrac{-(-15)+\sqrt{449}}{2\cdot8}=\dfrac{15+\sqrt{449}}{16}[/tex]