Quadratic equations take the form
(1) with
Any equation of this form may be solved using the formula
This formula is proved by completing the square for (1).
Starting from
divide through by a to give
(2) then write
Substitute this into (2) to give
Now make x the subject. Start by moving the last two terms to the right hand side.
Collect the terms on the right by adding them as fractions.
Square root both sides to give
Subtraction of
gives