we have the equation

Rewrite

Multiply both sides by cosx


Change the variable
u=cosx
substitute

Solve the quadratic equation
using the formula
a=-9
b=21
c=-12
substitute
![u=\frac{-21\pm\sqrt[]{21^2-4(-9)(-12)}}{2(-9)}](https://img.qammunity.org/2023/formulas/mathematics/college/5d2r1xphe0d0hsh21go20qk3umdw5d9wzx.png)
![\begin{gathered} u=\frac{-21\pm\sqrt[]{9}}{-18} \\ \\ u=(-21\pm3)/(-18) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/mgltmz9rah3ppe62ndafmwsejwmsx5t98j.png)
The values of u are
u=1 and u=4/3
Remember that
u=cosx
For u=1
the interval is [0,360) ----> the value of 360 degrees is not included
cosx=1 ------> the value of x=0 degrees
For u=4/3
cosx=4/3 -------> is not a solution (cosine cannot be greater than 1)
therefore
The solution is x=0 degrees