Question

what method most efficient to use to solve x^2+4x+3=0

Answer 1

My recommendation would be to factor..
x² + 4x + 3 = 0 factor the left side into two binomials
(x + 3)(x + 1) = 0 set each of these binomials equal to zero and solve

x + 3 = 0 Implies x = -3
x + 1 = 0 implies x = -1