1.) 2Q^2 = 400 + Q

2Q^2 - Q - 400 = 0

Use quadratic formula on the above;

You'll get roughly: Q = -13.89 V Q = 14.39

Q = (-sqrt(3209) + 1)/4 V Q = (sqrt(3201) + 1)/4, respectively, to be precise.

2.) (20 + 5Q + 500)/Q = 20 + 10Q

20 + 5Q + 500 = 20Q + 10Q^2

520 - 15Q = 10Q^2

0 = 10Q^2 + 15Q - 520

Again, use quadratic formula;

Q = -8 V Q = 13/2