This is my own artistic rendering of a nomogram by ET Whittaker for solving quadratic equations. The swirly and spiky parts are all razzle-dazzle. The only mathematically meaningful part is the marked scales.
Here is a short video about the nomogram:
You need a string or straight-edge to line up your points.
To solve the quadratic x2+ax+b=0, line up the string or straight edge from the number a on the horizontal axis to the number b on the vertical axis. The solutions x will be the points where the string intersects the curved scale.
This PDF is meant to be printed two-sided to get some information on the back. It can be rescaled without messing up the accuracy.