Making $r$ the subject of a formula

Question

Making r the subject

$ S = 2xr^2 + xrl $

On the right side of the equation , I factorise $r$-

$ r ( 2xr + xl ) $

I realised that I still have a $r$ inside $2xr$ . How do I remove that $r$ ? Thanks for the help !

Answer 1

$$2xr^2 + xlr-S=0$$

Now solve using the quadratic formula with $a=2x$ ,$b=xl$, $c=-S$. Or by completing the square.

Answer 2

You have a quadratic equation $2xr^2+xrl-S=0$ and can use the quadratic formula to get $r=\frac 1{4x}(-xl\pm\sqrt{r^2l^2-4\cdot 2x \cdot S})$