Answer:
....x = the number of years sought
in x years the eldest will have x+13, the youngest x+7
we are looking in how many years the product of their ages will be 280
(x+13)(x+7)=280
x²+7x+13x+91=280
x²+20x+91-280 =0
x²+20x-189 =0
b²-4ac = 20²-4(1*-189)=1156
Δ=1156; √Δ=34
(-b-√Δ)/2a =(-20-34)/2=-27
(-b+√Δ)/2a = (-20+34)/2 =7
the number of years cannot be negative
it is in 7 years that the product of their ages will be 280
to be checked :
(13+7)(7+7) = 20*14=280
Explanation: