The problem with dividing an equations or even a function by the independant variable desired to solve for, you lose one of the values which is contained in the set of the solution.
So, if you have:
\[f:f(x)=12- \frac{ x^2 }{ 2 }\]
And we are asked to find the value that the function takes when x is equal to 2k, or in other words f(2k).
\[f(2k)=12-\frac{ (2k)^2 }{ 2 }\]
\[f(2k)=2k\]
Then, knowing the value the function takes at the point "2k", we only need to find the value of "k" that satisfies this equation:
\[2k=12-\frac{ (2k)^2 }{ 2 }\]
This has become a univariable equation but as a second degree polynomial expression, so what we will do is try to fix to the structure:
\[ax^2+bx+c=0\]
in this case, "k" is the variable so we will treat it as if it was a popular known "x" first off, getting rid of the denominator by performing the common denominator operation:
\[2k=\frac{ 2(12)-(2k)^2 }{ 2 }\]
And multiply both sides by "2":
\[2(2k)=2(12)-(2k)^2\]
And now, simplifying:
\[4k=24-4k^2\]
And taking it to the structure I mentioned earlier:
\[4k^2+4k-24=0\]
And we can divide both sides by "4" in order to reduce the coefficients as much as possible:
\[\frac{ 4k^2+4k-24 }{ 4 }=\frac{ 0 }{ 4 }\]
and simplifying:
\[k^2+k-6=0\]
Now, in order to solve this we will have to use the general formula or also known as the "formula of bhaskara".