Let x 2+3x- 1 = y, then the original equation is deformed as: y+8 under the root sign minus y-8=2 under the root sign.

Two-sided square: Y 2-64 = 4 under the radical sign of 2y-2 times, ranking: Y 2-64 = Y-2 under the radical sign.

Quadratic on both sides: y 2-64 = y 2-4y+4, that is, y = 65, y = 17.

X 2+3x- 1 = 17 solution: x 1=3, x2=-6.

It is proved that X 1 and X2 are the roots of the original equation.