Notice that the expression:
[tex]3m^2-24m+27=0[/tex]
has all coefficients divisible by 3, then we can simplify the equation like this:
[tex]\begin{gathered} 3m^2-24m+27=3\cdot(m^2-8m+9)=0 \\ \Rightarrow m^2-8m+9=0 \end{gathered}[/tex]
then, using the quadratic formula, we have the following:
[tex]\begin{gathered} m_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ a=1 \\ b=-8 \\ c=9 \\ \Rightarrow m_{1,2}=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(9)}}{2(1)}=\frac{8\pm\sqrt[]{64-36}}{2} \\ =\frac{8\pm\sqrt[]{28}}{2} \\ \Rightarrow m_1=\frac{8+\sqrt[]{28}}{2}=6.64 \\ \Rightarrow m_2=\frac{8-\sqrt[]{28}}{2}=1.35 \\ _{} \end{gathered}[/tex]
therefore, the solution of the equation from the options is m=1.35
