Solution of a quadratic equation

In general case of a non-reduced quadratic equation:

ax ² + bx + c = 0 ,

its roots are found by the formula:

If to divide all terms of a non-reduced quadratic equation by  a (is it possible ?),  and to sign  b / a = p  and  c / a = q , then we’ll receive the reduced quadratic equation:

x ² + px + q = 0 ,

roots of which are calculated by the formula:
                                                       

E x a m p l e .   x ² + 5x + 6 = 0 .  Here  p = 5,  q = 6. Then we have: 

                        hence,   x₁= – 5 / 2  + 1 / 2  = – 2 ,    x₂ = – 5 / 2 – 1 / 2 = – 3

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