How to solve a quadratic equation

There are several problems in solving quadratic equations. Some of the more important ones are determining neater coefficients, numerics, and root ordering. Solving such problems requires the derivation of a homogeneous algorithm that uses the vector names instead of their values to emphasize the pattern. The [x1,w1] solution stays stable when B goes from positive to zero negative making sure that the [x1,w1] solution does not abruptly jump over to the other solution during transition. However, there is a jump via a homogenous scale when B passes zero and A = C , having good reason for picking one solution set over another. Finally, the two formulations for each of [x1,w1] and [x2,w2] are homogeneously equivalent; one is a scalar multiple of the other.