Amount of D in 5=100 (100/(25D+100)) power 4?

Question

Amount of D in 5=100 (100/(25D+100))power 4

Answer 1

5/100=(100/(25D+100))^4
1/20= (100/(25D+100))^4
(1/20)^(1/4)=100/(25D+100)
20^(1/4)=(25D+100)/100
100(20^(1/4)=25D+100
25D=(100(20^(1/4))-100
D=[(100(20^(1/4))-100]/25
D=4(20^(1/4))-4

Since 20^(1 / 4) = 2.11474253
D=4(2.11474253)-4
D=4.45897012

Therefore D is about 4.46 (alternatively you could leave it as the exact answer in the last step)

Answer 2

5=100(100/(25D+100))^4
5 = 100(100/25D + 100/100)^4
5 = 100(4/D + 1)^4
5/100 = (4/D + 1)^4
(1/20)^(1/4) = 4/D + 1
(1/20)^(1/4) = 4/D
D = 4/(1/20)^(1/4)
D = 4 / (500/10000)^(1/4)
D = 4 / (500)^(1/4)/10
D = 40 / (500)^1/4)
[500 = 2*2*5*5*5]
D = 40(20)^1/4/10
D = 4(20)^1/4
D = 8.45