21*a^2-4ab-b^2=0

Solution for 21*a^2-4ab-b^2=0 equation:

Simplifying
21a2 + -4ab + -1b2 = 0

Reorder the terms:
-4ab + 21a2 + -1b2 = 0

Solving
-4ab + 21a2 + -1b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + -1b)(7a + b) = 0

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

Simplifying
3a + -1b = 0

Solving
3a + -1b = 0

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

Add 'b' to each side of the equation.
3a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
3a + 0 = 0 + b
3a = 0 + b
Remove the zero:
3a = b

Divide each side by '3'.
a = 0.3333333333b

Simplifying
a = 0.3333333333b
Subproblem 2
Set the factor '(7a + b)' equal to zero and attempt to solve:

Simplifying
7a + b = 0

Solving
7a + b = 0

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

Add '-1b' to each side of the equation.
7a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
7a + 0 = 0 + -1b
7a = 0 + -1b
Remove the zero:
7a = -1b

Divide each side by '7'.
a = -0.1428571429b

Simplifying
a = -0.1428571429b
Solution
a = {0.3333333333b, -0.1428571429b}