(√(x²+2x+8))²=(12-2x-x²)².
x²+2x+8=144+4x²+x⁴-48x-24x²+4x³.
x²+2x+8-144+20x²-x⁴+48x-4x³=0.
21x²+50x-136-x⁴-4x³=0.
-x⁴-4x³+21x²+50x-136=0.
-x⁴+2x³-6x³+12x²+9x²-18x+68x-136=0.
-x³(x-2)-6x²(x-2)+9x(x-2)+68(x-2)=0.
-(x-2)(x³+6x²-9x-68)=0.
-(x-2)(x³+4x²+2x²+8x-17x-68)=0.
-(x-2)(x²(x+4)+2x(x+4)-17(x+4))=0.
-(x-2)(x+4)(x²+2x-17)=0.
-(x-2)=0. x1=2.
x+4=0 x2=-4.
x²+2x-17=0 x3=-1+3√2. x4=-1-3√2.