a)
(x-5)(x+5)=x^2-100x
x^2-25-x^2-100x=0
-100x=25
x=-\frac{25}{100}
x=-\frac{1}{4}
b)
(3-x)^2-(x+\frac{1}{3})^2=\frac{2}{9}
9-6x+x^2-(x^2+\frac{2}{3}x+\frac{1}{9})=\frac{2}{9}
9-6x+x^2-x^2-\frac{2}{3}x-\frac{1}{9}=\frac{2}{9}
-6\frac{2}{3}x=\frac{2}{9}+\frac{1}{9}-9
-\frac{20}{3}x=\frac{1}{3}-9 |*3
-20x=1-27
-20x=-26
x=\frac{-26}{-20}=\frac{13}{10}
x=1,3
c)
4(\frac{1}{2}x-3)^2=(2-x)^2
4(\frac{1}{4}x^2-\frac{6}{2}x+9)=4-4x+x^2
x^2-12x+36+4x-x^2=4 |-36
-8x=-32 |:(-8)
x=4
d)
4(x+2)^2-(2x-1)^2=-5
4(x^2+4x+4)-(4x^2-4x+1)=-5
4x^2+16x+16-4x^2+4x-1=-5
20x+15=-5 |-15
20x=-20
x=-1