(4.6-8n)0.5=3.8

Solution for (4.6-8n)0.5=3.8 equation:

Simplifying
(4.6 + -8n) * 0.5 = 3.8

Reorder the terms for easier multiplication:
0.5(4.6 + -8n) = 3.8
(4.6 * 0.5 + -8n * 0.5) = 3.8
(2.3 + -4n) = 3.8

Solving
2.3 + -4n = 3.8

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-2.3' to each side of the equation.
2.3 + -2.3 + -4n = 3.8 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + -4n = 3.8 + -2.3
-4n = 3.8 + -2.3

Combine like terms: 3.8 + -2.3 = 1.5
-4n = 1.5

Divide each side by '-4'.
n = -0.375

Simplifying
n = -0.375