What is the most simplest way of solving quadratic equations?

Use the quadratic formula. A calculator will help with the squares and fractions and especially with square roots.

If the equation is ax2 +bx +c = 0, then x = (-b +/- sqrt(b2-4ac))/2a.

With a simple equation like x2+5x-6=0, you can solve by factoring: (x+6)(x-1)=0 <=> x=-6 or x=1. However, the quadratic formula will work on any equation.