x^2-3xa-28a^2=0

Solution for x^2-3xa-28a^2=0 equation:

Simplifying
x2 + -3xa + -28a2 = 0

Reorder the terms:
-3ax + -28a2 + x2 = 0

Solving
-3ax + -28a2 + x2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-4a + -1x)(7a + -1x) = 0

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

Simplifying
-4a + -1x = 0

Solving
-4a + -1x = 0

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

Add 'x' to each side of the equation.
-4a + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-4a + 0 = 0 + x
-4a = 0 + x
Remove the zero:
-4a = x

Divide each side by '-4'.
a = -0.25x

Simplifying
a = -0.25x
Subproblem 2
Set the factor '(7a + -1x)' equal to zero and attempt to solve:

Simplifying
7a + -1x = 0

Solving
7a + -1x = 0

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

Add 'x' to each side of the equation.
7a + -1x + x = 0 + x

Combine like terms: -1x + x = 0
7a + 0 = 0 + x
7a = 0 + x
Remove the zero:
7a = x

Divide each side by '7'.
a = 0.1428571429x

Simplifying
a = 0.1428571429x
Solution
a = {-0.25x, 0.1428571429x}