(7a^2-2a+6)-(-5a^2+3)=0

Solution for (7a^2-2a+6)-(-5a^2+3)=0 equation:

Simplifying
(7a2 + -2a + 6) + -1(-5a2 + 3) = 0

Reorder the terms:
(6 + -2a + 7a2) + -1(-5a2 + 3) = 0

Remove parenthesis around (6 + -2a + 7a2)
6 + -2a + 7a2 + -1(-5a2 + 3) = 0

Reorder the terms:
6 + -2a + 7a2 + -1(3 + -5a2) = 0
6 + -2a + 7a2 + (3 * -1 + -5a2 * -1) = 0
6 + -2a + 7a2 + (-3 + 5a2) = 0

Reorder the terms:
6 + -3 + -2a + 7a2 + 5a2 = 0

Combine like terms: 6 + -3 = 3
3 + -2a + 7a2 + 5a2 = 0

Combine like terms: 7a2 + 5a2 = 12a2
3 + -2a + 12a2 = 0

Solving
3 + -2a + 12a2 = 0

Solving for variable 'a'.

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

Divide each side by '12'.
0.25 + -0.1666666667a + a2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -0.1666666667a + -0.25 + a2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -0.1666666667a + a2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -0.1666666667a + a2 = 0 + -0.25
-0.1666666667a + a2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-0.1666666667a + a2 = -0.25

The a term is -0.1666666667a.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667a + 0.006944444447 + a2 = -0.25 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667a + a2 = -0.25 + 0.006944444447

Combine like terms: -0.25 + 0.006944444447 = -0.243055555553
0.006944444447 + -0.1666666667a + a2 = -0.243055555553

Factor a perfect square on the left side:
(a + -0.08333333335)(a + -0.08333333335) = -0.243055555553

Can't calculate square root of the right side.

The solution to this equation could not be determined.