20=(b-3)*b*.5

Solution for 20=(b-3)*b*.5 equation:

Simplifying
20 = (b + -3) * b * 0.5

Reorder the terms:
20 = (-3 + b) * b * 0.5

Reorder the terms for easier multiplication:
20 = 0.5b(-3 + b)
20 = (-3 * 0.5b + b * 0.5b)
20 = (-1.5b + 0.5b2)

Solving
20 = -1.5b + 0.5b2

Solving for variable 'b'.

Reorder the terms:
20 + 1.5b + -0.5b2 = -1.5b + 1.5b + 0.5b2 + -0.5b2

Combine like terms: -1.5b + 1.5b = 0.0
20 + 1.5b + -0.5b2 = 0.0 + 0.5b2 + -0.5b2
20 + 1.5b + -0.5b2 = 0.5b2 + -0.5b2

Combine like terms: 0.5b2 + -0.5b2 = 0.0
20 + 1.5b + -0.5b2 = 0.0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
-40 + -3b + b2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -3b + 40 + b2 = 0 + 40

Reorder the terms:
-40 + 40 + -3b + b2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -3b + b2 = 0 + 40
-3b + b2 = 0 + 40

Combine like terms: 0 + 40 = 40
-3b + b2 = 40

The b term is -3b.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3b + 2.25 + b2 = 40 + 2.25

Reorder the terms:
2.25 + -3b + b2 = 40 + 2.25

Combine like terms: 40 + 2.25 = 42.25
2.25 + -3b + b2 = 42.25

Factor a perfect square on the left side:
(b + -1.5)(b + -1.5) = 42.25

Calculate the square root of the right side: 6.5

Break this problem into two subproblems by setting 
(b + -1.5) equal to 6.5 and -6.5.

Subproblem 1
b + -1.5 = 6.5

Simplifying
b + -1.5 = 6.5

Reorder the terms:
-1.5 + b = 6.5

Solving
-1.5 + b = 6.5

Solving for variable 'b'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + b = 6.5 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + b = 6.5 + 1.5
b = 6.5 + 1.5

Combine like terms: 6.5 + 1.5 = 8
b = 8

Simplifying
b = 8

Subproblem 2
b + -1.5 = -6.5

Simplifying
b + -1.5 = -6.5

Reorder the terms:
-1.5 + b = -6.5

Solving
-1.5 + b = -6.5

Solving for variable 'b'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + b = -6.5 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + b = -6.5 + 1.5
b = -6.5 + 1.5

Combine like terms: -6.5 + 1.5 = -5
b = -5

Simplifying
b = -5

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {8, -5}