3x^2-5a^2=(x+a)(x-a)

Solution for 3x^2-5a^2=(x+a)(x-a) equation:

Simplifying
3x2 + -5a2 = (x + a)(x + -1a)

Reorder the terms:
-5a2 + 3x2 = (x + a)(x + -1a)

Reorder the terms:
-5a2 + 3x2 = (a + x)(x + -1a)

Reorder the terms:
-5a2 + 3x2 = (a + x)(-1a + x)

Multiply (a + x) * (-1a + x)
-5a2 + 3x2 = (a(-1a + x) + x(-1a + x))
-5a2 + 3x2 = ((-1a * a + x * a) + x(-1a + x))

Reorder the terms:
-5a2 + 3x2 = ((ax + -1a2) + x(-1a + x))
-5a2 + 3x2 = ((ax + -1a2) + x(-1a + x))
-5a2 + 3x2 = (ax + -1a2 + (-1a * x + x * x))
-5a2 + 3x2 = (ax + -1a2 + (-1ax + x2))

Reorder the terms:
-5a2 + 3x2 = (ax + -1ax + -1a2 + x2)

Combine like terms: ax + -1ax = 0
-5a2 + 3x2 = (0 + -1a2 + x2)
-5a2 + 3x2 = (-1a2 + x2)

Solving
-5a2 + 3x2 = -1a2 + x2

Solving for variable 'a'.

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

Add 'a2' to each side of the equation.
-5a2 + a2 + 3x2 = -1a2 + a2 + x2

Combine like terms: -5a2 + a2 = -4a2
-4a2 + 3x2 = -1a2 + a2 + x2

Combine like terms: -1a2 + a2 = 0
-4a2 + 3x2 = 0 + x2
-4a2 + 3x2 = x2

Add '-3x2' to each side of the equation.
-4a2 + 3x2 + -3x2 = x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-4a2 + 0 = x2 + -3x2
-4a2 = x2 + -3x2

Combine like terms: x2 + -3x2 = -2x2
-4a2 = -2x2

Divide each side by '-4'.
a2 = 0.5x2

Simplifying
a2 = 0.5x2

Take the square root of each side:
a = {-0.707106781x, 0.707106781x}