We will assume that the leading coefficient is positive. While I can understand the impulse showing students how the Formula was invented and thereby providing a concrete example of the usefulness of abstract symbolic manipulation the computations involved are often a bit beyond the average student at this point. Isolate the variable terms on one side and the constant terms on the other.
Is actually derived using the steps involved in completing the square.
Given latexax2bxc0latex latexane 0latex we will complete the square as follows. Finally isolate x and write the right side under a common denominator again. Next write the right side of the equation under a common denominator and take the square root of each side. Iii Complete the square by adding the square of one-half of the coefficient of x this is the square of b 2 a to both sides.