20a^2-41ab+20b^2=0

Solution for 20a^2-41ab+20b^2=0 equation:

Simplifying
20a2 + -41ab + 20b2 = 0

Reorder the terms:
-41ab + 20a2 + 20b2 = 0

Solving
-41ab + 20a2 + 20b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a + -5b)(5a + -4b) = 0

Subproblem 1
Set the factor '(4a + -5b)' equal to zero and attempt to solve:

Simplifying
4a + -5b = 0

Solving
4a + -5b = 0

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

Add '5b' to each side of the equation.
4a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
4a + 0 = 0 + 5b
4a = 0 + 5b
Remove the zero:
4a = 5b

Divide each side by '4'.
a = 1.25b

Simplifying
a = 1.25b
Subproblem 2
Set the factor '(5a + -4b)' equal to zero and attempt to solve:

Simplifying
5a + -4b = 0

Solving
5a + -4b = 0

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

Add '4b' to each side of the equation.
5a + -4b + 4b = 0 + 4b

Combine like terms: -4b + 4b = 0
5a + 0 = 0 + 4b
5a = 0 + 4b
Remove the zero:
5a = 4b

Divide each side by '5'.
a = 0.8b

Simplifying
a = 0.8b
Solution
a = {1.25b, 0.8b}