Solve the equation $|2x^2+x-1|=|x^2+4x+1|$ Find the sum of all the solutions of the equation  $|2x^2+x-1|=|x^2+4x+1|$
Though I tried to solve it in desmos.com and getting the requisite answer but while solving it manually it is getting very lengthy. 
I tried to construct the two parabola and mirror image the region below y axis but still getting it is getting complicated. 

Is there any easy method to solve it and get the sum of all the solutions ?


$$
|2x^2+x-1|=|x^2+4x+1|\\
(2x^2+x-1)^2=(x^2+4x+1)^2\\
(2x^2+x-1)^2-(x^2+4x+1)^2=0\\
[(2x^2+x-1)+(x^2+4x+1)]\cdot[(2x^2+x-1)-(x^2+4x+1)]=0\\
(3x^2+5x)\cdot(x^2-3x-2)=0\\
x\cdot(3x+5)\cdot(x^2-3x-2)=0\\
Solving\space for\space all\space cases,\space we\space get:\\
x=0\\
x=-\frac{5}{3}\\
x=\frac{3\pm\sqrt{17}}{2}
$$
