When you have x^2 and x in the same equality put always everything =0.
Why not isolate x from the beggining, well because we have different powers of x and which one do we isolate... Beep! can't do.
So, we use the trick putting everything=0. So we transfer the 6x (which is positive it gets negative on the other side and the opposite goes with the -2x^2). We get : 4x^2+17x-6x+2x^2=0 (nothing left on the right).
We add the x^2 together and the x together and get 6x^2+11x=0 so we take out an x and get x(6x+11)=0 so to get 0 we must have either x=0 or (6x+11)=0. So if x=0 well, x=0. And if 6x+11=0 so x=-11/6. So two possible answer: 0 or -11/6. No square roots needed.
Try them in 4x^2+17x=6x-2x^2 and you'll get an equality (either all x=0 or all x = -11/6 not at the same time) !!!