is the quadratic equation appropriate for this? I work in a paper mill as a tech. There is a formula for percent solvents in a liquor solution. It is s=(A*P^2) + (B*P)
$S$ is the percent solvent, $A$ and $B$ are constants, $3.21953$ and $8.117$ respectively. I would like to solve for $p$, as instrumentation can tell me percent solvents, but I would like to verify the percentage for calibration purposes. I started moving stuff around and got confused, as college math classes were quite some time ago. I get that there is a squared variable there, so I have to square root something, and that percent solvents will never be negative, so that's probably an absolute value. This looks like a quadratic equation to me, if I replace the coefficients to $P^2$ and $p$ with $a$,$b$, and call percent solvents ($s$) $c$. 
So then I subtracted $s$, and get $0= AP^2+Bp -C$. cool. So then I assumed I could use the quadratic equation, 
$P= \frac{-b \pm \sqrt{b^2+4ac}}{2a}$.
Is this a safe assertion? Or have I misused this formula?
(also if someone who knows how to format math on this website were to come tidy this up for me it would be much appreciated. 

Yes, this is how it would be done.
You would then have $\displaystyle P = \frac{-B \pm \sqrt{B^2-4As}}{2A}$.
When you evaluate both the $+$ and $-$, make sure you pick the $P$ for which the percent solvent makes sense physically. 
