See if your final equation is quadratic in the form

Ax^2 +Bx +C = 0

Then, yes, you can use the Quadratic formula to find x.

Closed right circular cylinder 15cm high, 1500sq.cm total surface area, and radius r.

Find r.

1500 = (2pi*r)(15) + 2(pi*r^2)

Umm, yes, you can use the Quadratic formula here.

1500 = 30pi*r +2pi*r^2

2pi*r^2 +30pi*r -1500 = 0

r = {-30pi +,-sqrt[(30pi)^2 -4(2pi)(-1500)]} / 2(2pi)

r = {-94.2478 +,-215.8281} /12.5664

r = 9.675cm or -24.675cm

Reject the r = -24.675cm because there are no negative dimensions.

Therefore, r = 9.675cm ---------------answer.