Question: how to solve quadratic equation very fast?
Answer: There are several ways to solve them (unless you have one with imaginary or complex solutions——- for these, the quadratic equation is the easiest). ... 
Solve x^2+3x+2=0.
Method 1: Factor x^2+3x+2 into (x+1)(x+2) and then solve (x+1)(x+2)=0. ... 
Method 2: Graph y=x^2+3x+2 and see the x-intercepts are at x=-1 and x=-2.