[tex]\left \{ {{ab=15(a+b)} \atop {a+2b=100}} \right.[/tex]

[tex]\left \{ {{ab = 15a+15b} \atop {a=100-2b}} \right.[/tex]

[tex]b(100-2b) = 15(100-2b) +15b\\100b - 2b^2 = 1500-30b+15b\\-2b^2+115b-1500=0\\D = 115^2-4*2*1500 = 13225-12000 = 1225=35^2\\b_1 = \frac{-115-35}{-4} = 37.5\\ b_2 = \frac{-115+35}{-4} = 20\\ \\a_1 = 100-2*37.5=25\\a_2 = 100-2*20 = 60\\\\(a_1;b_1) = (25;37.5)\\(a_2;b_2) = (60;20)[/tex]