^ - степень.
(x^2+2x)^2-5x^2-10x+4=0
x^4+2*2x*x^2+4x^2-5x^2-10x+4=0
x^4+4x^3-x^2-10x+4=0
x^4+2x^3+2x^3-x^2+4x^2-4x^2-2x-8x+4=0
x^2(x^2+2x-1)+2x(x^2+2x-1)-4(x^2+2x-1)=0
(x^2+2x-1)(x^2+2x-4)=0
x^2+2x-1=0
D^2=4+4=8, D= +-2√2
x1=(-2+2√2):2=-1+√2
x2=-1-√2
x^2+2x-4=0
D^2=4+16=20, D=+-2√5
x3=(-2+2√5):2=-1+√5
x4=-1-√5
x1,x2,x3,x4 - корни уровнения:
x1=-1+√2
x2=-1-√2
x3=-1+√5
x4=-1-√5