c$.$ Solve the following quadratic problem using the quadratic formula. A site engineer is measuring a $5m$ high tank, made up from a cylinder below a dome top, the height of the cylinder section is $h,$ a dome radius $r$ and a surface area of $138m^2.$

Using Quadratic Equations $($common formula$)$ calculate the radius $r$ of the tank where

$h=5-r$

$3r^2+2rh=138$

Check and evaluate your answer.