Make r the Subject of the formula

Question

Make r the subject of the formula S=πrl+ πr^2. The answer should be $r=\frac{-\pi l+\sqrt{\pi^{2} I^{2}+4 S \pi}}{2 \pi}$ I cant figure out how they got the answer. Please help

Answer 1

You have an equation of the form :

$a x^2 + b x + c = 0$

which can be written :

$(x + {b\over2a})^2 ={b^2 - 4ac\over 4a^2}$

If $b^2 - 4ac$ is positive, you can take the square root, thus :

$x + {b\over 2a} = \pm {\sqrt{b^2 - 4ac}\over 2a}$ ie $x = {-b \pm \sqrt{b^2 - 4ac}\over 2a}$