(ax-b)(ax-b)+(bx-a)(bx-a)=x

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Solution for (ax-b)(ax-b)+(bx-a)(bx-a)=x equation: 


Simplifying
(ax + -1b)(ax + -1b) + (bx + -1a)(bx + -1a) = x

Multiply (ax + -1b) * (ax + -1b)
(ax(ax + -1b) + -1b * (ax + -1b)) + (bx + -1a)(bx + -1a) = x
((ax * ax + -1b * ax) + -1b * (ax + -1b)) + (bx + -1a)(bx + -1a) = x

Reorder the terms:
((-1abx + a2x2) + -1b * (ax + -1b)) + (bx + -1a)(bx + -1a) = x
((-1abx + a2x2) + -1b * (ax + -1b)) + (bx + -1a)(bx + -1a) = x
(-1abx + a2x2 + (ax * -1b + -1b * -1b)) + (bx + -1a)(bx + -1a) = x
(-1abx + a2x2 + (-1abx + 1b2)) + (bx + -1a)(bx + -1a) = x

Reorder the terms:
(-1abx + -1abx + a2x2 + 1b2) + (bx + -1a)(bx + -1a) = x

Combine like terms: -1abx + -1abx = -2abx
(-2abx + a2x2 + 1b2) + (bx + -1a)(bx + -1a) = x

Reorder the terms:
-2abx + a2x2 + 1b2 + (-1a + bx)(bx + -1a) = x

Reorder the terms:
-2abx + a2x2 + 1b2 + (-1a + bx)(-1a + bx) = x

Multiply (-1a + bx) * (-1a + bx)
-2abx + a2x2 + 1b2 + (-1a * (-1a + bx) + bx(-1a + bx)) = x
-2abx + a2x2 + 1b2 + ((-1a * -1a + bx * -1a) + bx(-1a + bx)) = x

Reorder the terms:
-2abx + a2x2 + 1b2 + ((-1abx + 1a2) + bx(-1a + bx)) = x
-2abx + a2x2 + 1b2 + ((-1abx + 1a2) + bx(-1a + bx)) = x
-2abx + a2x2 + 1b2 + (-1abx + 1a2 + (-1a * bx + bx * bx)) = x
-2abx + a2x2 + 1b2 + (-1abx + 1a2 + (-1abx + b2x2)) = x

Reorder the terms:
-2abx + a2x2 + 1b2 + (-1abx + -1abx + 1a2 + b2x2) = x

Combine like terms: -1abx + -1abx = -2abx
-2abx + a2x2 + 1b2 + (-2abx + 1a2 + b2x2) = x

Reorder the terms:
-2abx + -2abx + 1a2 + a2x2 + 1b2 + b2x2 = x

Combine like terms: -2abx + -2abx = -4abx
-4abx + 1a2 + a2x2 + 1b2 + b2x2 = x

Solving
-4abx + 1a2 + a2x2 + 1b2 + b2x2 = x

Solving for variable 'a'.

Combine like terms: x + -1x = 0
-4abx + 1a2 + a2x2 + 1b2 + b2x2 + -1x = 0

The solution to this equation could not be determined.

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