An agricultural fertigation method includes the continuous in situ manufacture of one or more nitrogen-nutrient raw fertilizers within the irrigation system upstream of the agricultural field being irrigated for a prolonged term. Raw materials, namely nitric acid, urea, ammonium hydroxide, calcium nitrate and/or magnesium nitrate, are intermixed with each other and/or with the stream of the flowing irrigation water. The stream of flowing irrigation water dampens the resultant dissolution exotherm. A system wherein raw materials are efficiently continuously fed to the irrigation system main line or a side-arm reactor efficiently implements the method.