The equation is given as,
[tex]-3x^2\: +\: 24x\: -\: 3\: \le-3\text{ }[/tex]
Rearranging the constant terms on both the sides,
[tex]\begin{gathered} -3x^2\: +\: 24x\: \le\text{ 0} \\ 3(-x^2\text{ + x ) }\le\text{ 0} \\ -x^2\text{ + x }\le\text{ 0} \end{gathered}[/tex]
Calculating the value of x ,
[tex]\begin{gathered} -\text{ x (x - 8) }\le\text{ 0} \\ (-x(x-8))(-1)\ge\text{ ( -1)} \end{gathered}[/tex]
Simplifying,
[tex]x(x-8)\text{ }\ge\text{ 0}[/tex]
Thus the intervals of x are,
[tex]x\text{ }\le\text{ 0 or x }\ge\text{ 8}[/tex]
