How to solve a quadratic equation without a calculator?

You factorise it. First, you find a common factor between a, b and c. Then, you find the 2 numbers that multiplied give you c and added give you b. If a=1, then the additive inverse of those 2 numbers are the answers. If a does not equal 1, you decompose b into the 2 numbers that multiplied give you c and added give you b. You find common factors and then you will find the answers.