Answer :
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Write the given quadratic equation.
[tex]9m^2-66m_{}+21=0[/tex]STEP 2: Write the quadratic formula
[tex](m_1,m_2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]STEP 3: Solve the given equation using the quadratic formula
[tex]\begin{gathered} 9m^2-66m_{}+21 \\ \text{From the }equation, \\ a=9,b=-66,c=21 \\ m_{1,\: 2}=\frac{-\left(-66\right)\pm\sqrt{\left(-66\right)^2-4\cdot\:9\cdot\:21}}{2\cdot\:9} \\ Simplify\sqrt[]{(-66)^2-4\cdot\: 9\cdot\: 21} \\ \sqrt[]{(-66)^2-4\cdot\: 9\cdot\: 21}=\sqrt[]{4356-756}=\sqrt[]{3600}=60 \\ \\ m_{1,\: 2}=\frac{-\left(-66\right)\pm\:60}{2\cdot\:9} \\ Separate\: the\: solutions \\ m_1=\frac{-\left(-66\right)+60}{2\cdot\:9},\: m_2=\frac{-\left(-66\right)-60}{2\cdot\:9} \\ m_1=\frac{-(-66)+60}{2\cdot\: 9}=\frac{66+60}{18}=\frac{126}{18}=7 \\ \: m_2=\frac{-(-66)-60}{2\cdot\: 9}=\frac{66-60}{18}=\frac{6}{18}=\frac{1}{3} \end{gathered}[/tex]Hence, the answer to the given quadratic equation is:
[tex]\begin{gathered} m=7 \\ m=\frac{1}{3} \end{gathered}[/tex]