a)
(x+2)^2-x^2>4
x^2+4x+4-x^2>4
4x>4-4
4x>0/:4
x>0
x\in(0;+\infty)
b)
(x-5)^2-x^2<21
x^2-10x+25-x^2<21
-10x<21-25
-10x<-4 /:(-10)
x>\frac{4}{10}
x>\frac{2}{5}
x\in(\frac{2}{5};+\infty)
http://www.wolframalpha.com/input/?i=(x-5)%5E2-x%5E2%3C21
c)
(x+4)(x-4)-x^2<2x
x^2-16-x^2-2x<0
-2x<16/:(-2)
x>-8
x\in(-8:+\infty)
http://www.wolframalpha.com/input/?i=(x%2B4)(x-4)-x%5E2%3C2x
d)
2(x-6)^2-2x^2\geq 10+7x
2(x^2-12x+36)-2x^2\geq10+7x
2x^2-24x+72-2x^2-7x\geq10
-31x\geq10-72
-31x\geq-62/:(-31)
x\leq2
x\in(-\infty;2\rangle
http://www.wolframalpha.com/input/?i=2(x-6)%5E2-2x%5E2%5Cgeq+10%2B7x