5b^2-12b-56=0

Solution for 5b^2-12b-56=0 equation:

Simplifying
5b2 + -12b + -56 = 0

Reorder the terms:
-56 + -12b + 5b2 = 0

Solving
-56 + -12b + 5b2 = 0

Solving for variable 'b'.

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

Divide each side by '5'.
-11.2 + -2.4b + b2 = 0

Move the constant term to the right:

Add '11.2' to each side of the equation.
-11.2 + -2.4b + 11.2 + b2 = 0 + 11.2

Reorder the terms:
-11.2 + 11.2 + -2.4b + b2 = 0 + 11.2

Combine like terms: -11.2 + 11.2 = 0.0
0.0 + -2.4b + b2 = 0 + 11.2
-2.4b + b2 = 0 + 11.2

Combine like terms: 0 + 11.2 = 11.2
-2.4b + b2 = 11.2

The b term is -2.4b.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4b + 1.44 + b2 = 11.2 + 1.44

Reorder the terms:
1.44 + -2.4b + b2 = 11.2 + 1.44

Combine like terms: 11.2 + 1.44 = 12.64
1.44 + -2.4b + b2 = 12.64

Factor a perfect square on the left side:
(b + -1.2)(b + -1.2) = 12.64

Calculate the square root of the right side: 3.555277767

Break this problem into two subproblems by setting 
(b + -1.2) equal to 3.555277767 and -3.555277767.

Subproblem 1
b + -1.2 = 3.555277767

Simplifying
b + -1.2 = 3.555277767

Reorder the terms:
-1.2 + b = 3.555277767

Solving
-1.2 + b = 3.555277767

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '1.2' to each side of the equation.
-1.2 + 1.2 + b = 3.555277767 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + b = 3.555277767 + 1.2
b = 3.555277767 + 1.2

Combine like terms: 3.555277767 + 1.2 = 4.755277767
b = 4.755277767

Simplifying
b = 4.755277767

Subproblem 2
b + -1.2 = -3.555277767

Simplifying
b + -1.2 = -3.555277767

Reorder the terms:
-1.2 + b = -3.555277767

Solving
-1.2 + b = -3.555277767

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '1.2' to each side of the equation.
-1.2 + 1.2 + b = -3.555277767 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + b = -3.555277767 + 1.2
b = -3.555277767 + 1.2

Combine like terms: -3.555277767 + 1.2 = -2.355277767
b = -2.355277767

Simplifying
b = -2.355277767

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {4.755277767, -2.355277767}