Question

Find the diameter of the base of a right cylinder if the surface area is 128(pi) and the height is 12cm.

Answer 1

$d=2r\\ A=128 \pi \\ A=2 \pi r^{2} +2 \pi rh \\\\ 2 \pi r^{2} +2 \pi rh = 128 \pi \\ 2 r^{2} +2rh = 128\\ 2 r^{2}+24r-128=0\\ r^{2}+12r-64=0\\ delta=400\\ r_{1/2} = -16/4 \\ r=4cm\\ d=8cm$

Radius / diameter as a length cannot be negative, that's why '-16' is wrong.