b^2+4b-6=0

Solution for b^2+4b-6=0 equation:

Simplifying
b2 + 4b + -6 = 0

Reorder the terms:
-6 + 4b + b2 = 0

Solving
-6 + 4b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 4b + 6 + b2 = 0 + 6

Reorder the terms:
-6 + 6 + 4b + b2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 4b + b2 = 0 + 6
4b + b2 = 0 + 6

Combine like terms: 0 + 6 = 6
4b + b2 = 6

The b term is 4b.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4b + 4 + b2 = 6 + 4

Reorder the terms:
4 + 4b + b2 = 6 + 4

Combine like terms: 6 + 4 = 10
4 + 4b + b2 = 10

Factor a perfect square on the left side:
(b + 2)(b + 2) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(b + 2) equal to 3.16227766 and -3.16227766.

Subproblem 1
b + 2 = 3.16227766

Simplifying
b + 2 = 3.16227766

Reorder the terms:
2 + b = 3.16227766

Solving
2 + b = 3.16227766

Solving for variable 'b'.

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

Add '-2' to each side of the equation.
2 + -2 + b = 3.16227766 + -2

Combine like terms: 2 + -2 = 0
0 + b = 3.16227766 + -2
b = 3.16227766 + -2

Combine like terms: 3.16227766 + -2 = 1.16227766
b = 1.16227766

Simplifying
b = 1.16227766

Subproblem 2
b + 2 = -3.16227766

Simplifying
b + 2 = -3.16227766

Reorder the terms:
2 + b = -3.16227766

Solving
2 + b = -3.16227766

Solving for variable 'b'.

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

Add '-2' to each side of the equation.
2 + -2 + b = -3.16227766 + -2

Combine like terms: 2 + -2 = 0
0 + b = -3.16227766 + -2
b = -3.16227766 + -2

Combine like terms: -3.16227766 + -2 = -5.16227766
b = -5.16227766

Simplifying
b = -5.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.16227766, -5.16227766}