What if Carl Friedrich Gauss was wrong?

What if Descartes and Gauss were completely wrong?
No, not about everything, obviously, but about some important details? What if there were two blunders hidden, correcting each other, according to the theory of compensated errors?
First blunder: after having understood that the real roots were revealed by x=[-b(+/-)sqrt(b²-4ac)]/2a, which is true and which is easily demonstrated, generalizing the same discriminant too quickly, without paying attention to the signs (complexes being complex to handle) and setting i²=-1 (which is true) then
x=[-b(+/-)i.sqrt(b²-4ac)]/2a instead of x=[-b(+/-)i.sqrt(b²+4ac)]/2a.
The complex root is no longer the same. There would therefore be a first error due to a misunderstood sign.
The error is then compensated by another sign error, during the proof by check via the reverse path. Thus, for me, the correct roots of f(x)=x²-2x+8 are x'=4i, and x"=2i which can easily be placed on the usual x'Ox axis of Cartesian coordinate systems, roots found elsewhere by using x=[-b(+/-)i.sqrt(b²+4ac)]/2a without being trapped by a sign error (we are no longer in real roots, but in complex roots, where x=-i on the x'Ox axis and vice versa).
R.H.