x^2-5a^2-4ax=0

Solution for x^2-5a^2-4ax=0 equation:

Simplifying
x2 + -5a2 + -4ax = 0

Reorder the terms:
-4ax + -5a2 + x2 = 0

Solving
-4ax + -5a2 + x2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1a + -1x)(5a + -1x) = 0

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

Simplifying
-1a + -1x = 0

Solving
-1a + -1x = 0

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

Add 'x' to each side of the equation.
-1a + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-1a + 0 = 0 + x
-1a = 0 + x
Remove the zero:
-1a = x

Divide each side by '-1'.
a = -1x

Simplifying
a = -1x
Subproblem 2
Set the factor '(5a + -1x)' equal to zero and attempt to solve:

Simplifying
5a + -1x = 0

Solving
5a + -1x = 0

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

Add 'x' to each side of the equation.
5a + -1x + x = 0 + x

Combine like terms: -1x + x = 0
5a + 0 = 0 + x
5a = 0 + x
Remove the zero:
5a = x

Divide each side by '5'.
a = 0.2x

Simplifying
a = 0.2x
Solution
a = {-1x, 0.2x}