7a*a-2a+9=2a*a+6a-6

Solution for 7a*a-2a+9=2a*a+6a-6 equation:

Simplifying
7a * a + -2a + 9 = 2a * a + 6a + -6

Multiply a * a
7a2 + -2a + 9 = 2a * a + 6a + -6

Reorder the terms:
9 + -2a + 7a2 = 2a * a + 6a + -6

Multiply a * a
9 + -2a + 7a2 = 2a2 + 6a + -6

Reorder the terms:
9 + -2a + 7a2 = -6 + 6a + 2a2

Solving
9 + -2a + 7a2 = -6 + 6a + 2a2

Solving for variable 'a'.

Reorder the terms:
9 + 6 + -2a + -6a + 7a2 + -2a2 = -6 + 6a + 2a2 + 6 + -6a + -2a2

Combine like terms: 9 + 6 = 15
15 + -2a + -6a + 7a2 + -2a2 = -6 + 6a + 2a2 + 6 + -6a + -2a2

Combine like terms: -2a + -6a = -8a
15 + -8a + 7a2 + -2a2 = -6 + 6a + 2a2 + 6 + -6a + -2a2

Combine like terms: 7a2 + -2a2 = 5a2
15 + -8a + 5a2 = -6 + 6a + 2a2 + 6 + -6a + -2a2

Reorder the terms:
15 + -8a + 5a2 = -6 + 6 + 6a + -6a + 2a2 + -2a2

Combine like terms: -6 + 6 = 0
15 + -8a + 5a2 = 0 + 6a + -6a + 2a2 + -2a2
15 + -8a + 5a2 = 6a + -6a + 2a2 + -2a2

Combine like terms: 6a + -6a = 0
15 + -8a + 5a2 = 0 + 2a2 + -2a2
15 + -8a + 5a2 = 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
15 + -8a + 5a2 = 0

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

Divide each side by '5'.
3 + -1.6a + a2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -1.6a + -3 + a2 = 0 + -3

Reorder the terms:
3 + -3 + -1.6a + a2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1.6a + a2 = 0 + -3
-1.6a + a2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1.6a + a2 = -3

The a term is -1.6a.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6a + 0.64 + a2 = -3 + 0.64

Reorder the terms:
0.64 + -1.6a + a2 = -3 + 0.64

Combine like terms: -3 + 0.64 = -2.36
0.64 + -1.6a + a2 = -2.36

Factor a perfect square on the left side:
(a + -0.8)(a + -0.8) = -2.36

Can't calculate square root of the right side.

The solution to this equation could not be determined.