x^2-5xs-24s^2=0

Solution for x^2-5xs-24s^2=0 equation:

Simplifying
x2 + -5xs + -24s2 = 0

Reorder the terms:
-5sx + -24s2 + x2 = 0

Solving
-5sx + -24s2 + x2 = 0

Solving for variable 's'.

Factor a trinomial.
(-3s + -1x)(8s + -1x) = 0

Subproblem 1
Set the factor '(-3s + -1x)' equal to zero and attempt to solve:

Simplifying
-3s + -1x = 0

Solving
-3s + -1x = 0

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

Add 'x' to each side of the equation.
-3s + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-3s + 0 = 0 + x
-3s = 0 + x
Remove the zero:
-3s = x

Divide each side by '-3'.
s = -0.3333333333x

Simplifying
s = -0.3333333333x
Subproblem 2
Set the factor '(8s + -1x)' equal to zero and attempt to solve:

Simplifying
8s + -1x = 0

Solving
8s + -1x = 0

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

Add 'x' to each side of the equation.
8s + -1x + x = 0 + x

Combine like terms: -1x + x = 0
8s + 0 = 0 + x
8s = 0 + x
Remove the zero:
8s = x

Divide each side by '8'.
s = 0.125x

Simplifying
s = 0.125x
Solution
s = {-0.3333333333x, 0.125x}