I have the following equations :
$$\begin{cases}K = \frac{B – 3}{20}\\ K = (20S+3)R+S\\ K = 20S^2 + (20N+7)S + N\\ N=S-R \end{cases}$$ - And I have the $B$ values, e.g : 173, 283, 2343, 834343
How can I find the $R$ values?
Another question: Can I re-write these equations as one equation (I want to use computer programming to find $R$ values) where the $R$ is the result and the $B$ is the variable?
You'll have $$K=40S^2+(8-20R)S-R$$ $$\iff K=40\left(\frac{K-3R}{20R+1}\right)^2+(8-20R)\cdot\frac{K-3R}{20R+1}-R$$ $$\iff K(20R+1)^2=40(K-3R)^2+(20R+1)(8-20R)(K-3R)-R(20R+1)^2$$ $$\iff 20K(20R+1)^2=800(K-3R)^2+20(20R+1)(8-20R)(K-3R)-20R(20R+1)^2$$ $$\iff \color{red}{20K}(20R+1)^2=2(\color{red}{20K}-60R)^2+(20R+1)(8-20R)(\color{red}{20K}-60R)-20R(20R+1)^2$$ $$\iff \color{red}{(B-3)}(20R+1)^2=2(\color{red}{B-3}-60R)^2+(20R+1)(8-20R)(\color{red}{B-3}-60R)-20R(20R+1)^2$$ $$\iff 16000 R^3+(400-800B) R^2+(-80-140B) R+2B^2-5B-3 = 0.$$