5a^2+24ab-5b^2=0

Solution for 5a^2+24ab-5b^2=0 equation:

Simplifying
5a2 + 24ab + -5b2 = 0

Reorder the terms:
24ab + 5a2 + -5b2 = 0

Solving
24ab + 5a2 + -5b2 = 0

Solving for variable 'a'.

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

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

Simplifying
5a + -1b = 0

Solving
5a + -1b = 0

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

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

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

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

Simplifying
a = 0.2b
Subproblem 2
Set the factor '(a + 5b)' equal to zero and attempt to solve:

Simplifying
a + 5b = 0

Solving
a + 5b = 0

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

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

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

Simplifying
a = -5b
Solution
a = {0.2b, -5b}