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Requires: Algebraic language

Solution of the quadratic equation, making use of the identity

$S^2-R^2=4P$

i.e.: for any couple of numbers, the square of the sum minus the square of the difference is four times the product. From this is easy to go to the quadratic formula

$x={ -b \pm \sqrt{ b^2 - 4ac} \over 2a }$