20a^2-31ab-7b^2=0

Solution for 20a^2-31ab-7b^2=0 equation:

Simplifying
20a2 + -31ab + -7b2 = 0

Reorder the terms:
-31ab + 20a2 + -7b2 = 0

Solving
-31ab + 20a2 + -7b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a + -7b)(5a + b) = 0

Subproblem 1
Set the factor '(4a + -7b)' equal to zero and attempt to solve:

Simplifying
4a + -7b = 0

Solving
4a + -7b = 0

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

Add '7b' to each side of the equation.
4a + -7b + 7b = 0 + 7b

Combine like terms: -7b + 7b = 0
4a + 0 = 0 + 7b
4a = 0 + 7b
Remove the zero:
4a = 7b

Divide each side by '4'.
a = 1.75b

Simplifying
a = 1.75b
Subproblem 2
Set the factor '(5a + b)' equal to zero and attempt to solve:

Simplifying
5a + b = 0

Solving
5a + b = 0

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

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

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

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

Simplifying
a = -0.2b
Solution
a = {1.75b, -0.2b}