9a^2+5ab-4b^2=0

Solution for 9a^2+5ab-4b^2=0 equation:

Simplifying
9a2 + 5ab + -4b2 = 0

Reorder the terms:
5ab + 9a2 + -4b2 = 0

Solving
5ab + 9a2 + -4b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(9a + -4b)(a + b) = 0

Subproblem 1
Set the factor '(9a + -4b)' equal to zero and attempt to solve:

Simplifying
9a + -4b = 0

Solving
9a + -4b = 0

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

Add '4b' to each side of the equation.
9a + -4b + 4b = 0 + 4b

Combine like terms: -4b + 4b = 0
9a + 0 = 0 + 4b
9a = 0 + 4b
Remove the zero:
9a = 4b

Divide each side by '9'.
a = 0.4444444444b

Simplifying
a = 0.4444444444b
Subproblem 2
Set the factor '(a + b)' equal to zero and attempt to solve:

Simplifying
a + b = 0

Solving
a + b = 0

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

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

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

Simplifying
a = -1b
Solution
a = {0.4444444444b, -1b}