You have 3 variables (a, b, x) but only 1 equation. Normally it takes the same number of equations as variables to solve. A bit of quick checking. . .
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5bx - 6a = -3b - 4ax
5bx + 4ax = 6a - 3b
(5b + 4a)x = 6a - 3b
x = (6a - 3b) / (5b + 4a)
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5x - 1 = -3b - 4ax
5x + 4ax = 1 - 3b
(5 + 4a)x = 1 - 3b
x = (1 - 3b) / (5 + 4a)
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(6a - 3b) / (5b + 4a) = (1 - 3b) / (5 + 4a)
(6a - 3b) (5 + 4a) = (1 - 3b) (5b + 4a)
30a + 24a^2 - 15b - 12ab = 5b + 4a - 15b^2 - 12ab
30a + 24a^2 - 15b = 5b + 4a - 15b^2
24a^2 + 26a - 20b + 15b^2 = 0
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With one equation we can eliminate 1 variable, but since we started with 3 variables, we're still left with 2 variables.