It's a quadratic equation. Solve it through factorisation.
5s^2 - 14s - 3 = 0
(5s + 1)(s - 3) = 0
5s + 1 = 0
or
s - 3 = 0
Therefore
s = -1/5
or
s = 3
All makes sense pretty sure it is 24
Yes, you can see by subtracting 32 from the bottom sides and seeing that the correspondent for 20 degrees celcius is double that of the correspondent for 10 degrees celcius