Anecdotes please - quadratic equations in real life

[Johnh]

In structural engineering design, there is a daily need to calculate the area of steel reinforcement required to achieve a given bending strength in a reinforced concrete beam of known size. This involves the area and yield strength of the steel, multiplied by a lever arm from the centroid of the steel to that of the compression block in the concrete. The more steel required the deeper is the compression block required to balance it and so the shorter is the lever arm. Hence there are depth-squared terms in the relationship. To solve it so that steel area is the solution, it becomes a quadratic.

TBH, a design engineer will not be punching numbers into the quadratic solution formula every day, but such a solution will be implied within whatever software is used.It will also be required when coding such software or setting up spreadsheets (or calc programs for the oldies). And it's also a necessary insight when learning the principles of concrete design in engineering education.