(7a^2-5a+6)-(9a-7a^2-7)=0

Solution for (7a^2-5a+6)-(9a-7a^2-7)=0 equation:

Simplifying
(7a2 + -5a + 6) + -1(9a + -7a2 + -7) = 0

Reorder the terms:
(6 + -5a + 7a2) + -1(9a + -7a2 + -7) = 0

Remove parenthesis around (6 + -5a + 7a2)
6 + -5a + 7a2 + -1(9a + -7a2 + -7) = 0

Reorder the terms:
6 + -5a + 7a2 + -1(-7 + 9a + -7a2) = 0
6 + -5a + 7a2 + (-7 * -1 + 9a * -1 + -7a2 * -1) = 0
6 + -5a + 7a2 + (7 + -9a + 7a2) = 0

Reorder the terms:
6 + 7 + -5a + -9a + 7a2 + 7a2 = 0

Combine like terms: 6 + 7 = 13
13 + -5a + -9a + 7a2 + 7a2 = 0

Combine like terms: -5a + -9a = -14a
13 + -14a + 7a2 + 7a2 = 0

Combine like terms: 7a2 + 7a2 = 14a2
13 + -14a + 14a2 = 0

Solving
13 + -14a + 14a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
14 the coefficient of the squared term: 

Divide each side by '14'.
0.9285714286 + -1a + a2 = 0

Move the constant term to the right:

Add '-0.9285714286' to each side of the equation.
0.9285714286 + -1a + -0.9285714286 + a2 = 0 + -0.9285714286

Reorder the terms:
0.9285714286 + -0.9285714286 + -1a + a2 = 0 + -0.9285714286

Combine like terms: 0.9285714286 + -0.9285714286 = 0.0000000000
0.0000000000 + -1a + a2 = 0 + -0.9285714286
-1a + a2 = 0 + -0.9285714286

Combine like terms: 0 + -0.9285714286 = -0.9285714286
-1a + a2 = -0.9285714286

The a term is -1a.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1a + 0.25 + a2 = -0.9285714286 + 0.25

Reorder the terms:
0.25 + -1a + a2 = -0.9285714286 + 0.25

Combine like terms: -0.9285714286 + 0.25 = -0.6785714286
0.25 + -1a + a2 = -0.6785714286

Factor a perfect square on the left side:
(a + -0.5)(a + -0.5) = -0.6785714286

Can't calculate square root of the right side.

The solution to this equation could not be determined.