Question Number 92489 by ajfour last updated on 07/May/20
$$\left(\mathrm{3}+\frac{{cq}}{\mathrm{12}{b}}\right){s}^{\mathrm{2}} +\frac{\mathrm{6}{c}}{{b}}{s}+\left(\frac{\mathrm{8}{c}^{\mathrm{2}} }{\mathrm{3}{b}^{\mathrm{2}} }−{b}\right)=\mathrm{0} \\ $$$$\left(\mathrm{1}+\frac{{cq}}{\mathrm{4}{b}}\right){s}^{\mathrm{2}} +\frac{\mathrm{3}{c}}{{b}}\left(\mathrm{1}−\frac{{cq}}{\mathrm{12}{b}}\right){s}+\left(\frac{\mathrm{12}{c}^{\mathrm{2}} }{{b}^{\mathrm{2}} }−{b}\right)=\mathrm{0} \\ $$$${solve}\:{simultaneously}\:{for}\:\boldsymbol{{q}}\:{and}\:\boldsymbol{{s}} \\ $$$${in}\:{terms}\:{of}\:{b}\:{and}\:{c}. \\ $$