I need to solve the following equation for the variable $f$:
$a=-f^2\cdot\cos(b+c\cdot f)+f$
It's been a long time since my last math class. I have a clue how to solve a quadratic equation, but that cosine makes it a hard nut for me. Can anyone please nudge me in the right direction on how to solve it? Is it even possible?
There is no closed-form solution. You could solve it as a series in powers of $a$: $$ f = a+\cos \left( b \right) {a}^{2}+ \left( \cos \left( 2\,b \right) +1- \sin \left( b \right) c \right) {a}^{3}+ \left( \frac54\,\cos \left( 3\,b \right) +{\frac {15}{4}\cos \left( b \right)}-\frac{5c}2\sin \left( 2 \,b \right) -\frac{c^2}{2}\cos \left( b \right) \right) {a}^{4} + \ldots $$
Or, given numerical values of $a,b,c$, you could use numerical methods such as Newton's method.