in Babylonian times (around 4000 years ago) there is evidence from a number of tablets that there were techniques used that involved forming and solving quadratic equations
this study seems to have arisen and developed in connection with a need to divide up land fairly (for inheritance purposes)
one of the shapes regularly involved was the right trapezium
suppose you have a piece of land that you know the area of
you know about the slope of a line, translated as a 'feed'
you want to find the width of a strip
deduct the area of the right-angled triangle (the height of which is found from the known 'feed')
and you are left with a known area 'R' (e.g one fifth of a total area)
so a quadratic equation was created (born) to find the value of 's'