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

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

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

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

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

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

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

Combine like terms: 6 + 7 = 13
13 + -3a + -3a + 5a2 + -2a2 = 0

Combine like terms: -3a + -3a = -6a
13 + -6a + 5a2 + -2a2 = 0

Combine like terms: 5a2 + -2a2 = 3a2
13 + -6a + 3a2 = 0

Solving
13 + -6a + 3a2 = 0

Solving for variable 'a'.

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

Divide each side by '3'.
4.333333333 + -2a + a2 = 0

Move the constant term to the right:

Add '-4.333333333' to each side of the equation.
4.333333333 + -2a + -4.333333333 + a2 = 0 + -4.333333333

Reorder the terms:
4.333333333 + -4.333333333 + -2a + a2 = 0 + -4.333333333

Combine like terms: 4.333333333 + -4.333333333 = 0.000000000
0.000000000 + -2a + a2 = 0 + -4.333333333
-2a + a2 = 0 + -4.333333333

Combine like terms: 0 + -4.333333333 = -4.333333333
-2a + a2 = -4.333333333

The a term is -2a.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2a + 1 + a2 = -4.333333333 + 1

Reorder the terms:
1 + -2a + a2 = -4.333333333 + 1

Combine like terms: -4.333333333 + 1 = -3.333333333
1 + -2a + a2 = -3.333333333

Factor a perfect square on the left side:
(a + -1)(a + -1) = -3.333333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.