a)
2-x=\frac{1}{2}(x+1)^2-\frac{(x-\sqrt7)(x+\sqrt7)}{2}|*2
4-2x=(x+1)^2-(x-\sqrt7)(x+\sqrt7)
4-2x=x^2+2x+1-(x^2-7)
4-2x=x^2+2x+1-x^2+7
4-2x=2x+8
-4x=4|:4
x=-1
b)
(1+x)^2+3x^2<(2x-1)^2+7
1+2x+x^2+3x^2<4x^2-4x+1+7
4x^2+2x+1<4x^2-4x+8
2x+1+4x<8
6x<7
x<\frac{7}{6}
x<1\frac{1}{6}
x\in (-\infty;1\frac{1}{6})