x^2-14k^2=5kx

Solution for x^2-14k^2=5kx equation:

Simplifying
x2 + -14k2 = 5kx

Reorder the terms:
-14k2 + x2 = 5kx

Solving
-14k2 + x2 = 5kx

Solving for variable 'k'.

Reorder the terms:
-5kx + -14k2 + x2 = 5kx + -5kx

Combine like terms: 5kx + -5kx = 0
-5kx + -14k2 + x2 = 0

Factor a trinomial.
(-2k + -1x)(7k + -1x) = 0

Subproblem 1
Set the factor '(-2k + -1x)' equal to zero and attempt to solve:

Simplifying
-2k + -1x = 0

Solving
-2k + -1x = 0

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

Add 'x' to each side of the equation.
-2k + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-2k + 0 = 0 + x
-2k = 0 + x
Remove the zero:
-2k = x

Divide each side by '-2'.
k = -0.5x

Simplifying
k = -0.5x
Subproblem 2
Set the factor '(7k + -1x)' equal to zero and attempt to solve:

Simplifying
7k + -1x = 0

Solving
7k + -1x = 0

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

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

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

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

Simplifying
k = 0.1428571429x
Solution
k = {-0.5x, 0.1428571429x}