0=-0.1d^2+0.5d+0.6

Solution for 0=-0.1d^2+0.5d+0.6 equation:

Simplifying
0 = -0.1d2 + 0.5d + 0.6

Reorder the terms:
0 = 0.6 + 0.5d + -0.1d2

Solving
0 = 0.6 + 0.5d + -0.1d2

Solving for variable 'd'.

Combine like terms: 0 + -0.6 = -0.6
-0.6 + -0.5d + 0.1d2 = 0.6 + 0.5d + -0.1d2 + -0.6 + -0.5d + 0.1d2

Reorder the terms:
-0.6 + -0.5d + 0.1d2 = 0.6 + -0.6 + 0.5d + -0.5d + -0.1d2 + 0.1d2

Combine like terms: 0.6 + -0.6 = 0.0
-0.6 + -0.5d + 0.1d2 = 0.0 + 0.5d + -0.5d + -0.1d2 + 0.1d2
-0.6 + -0.5d + 0.1d2 = 0.5d + -0.5d + -0.1d2 + 0.1d2

Combine like terms: 0.5d + -0.5d = 0.0
-0.6 + -0.5d + 0.1d2 = 0.0 + -0.1d2 + 0.1d2
-0.6 + -0.5d + 0.1d2 = -0.1d2 + 0.1d2

Combine like terms: -0.1d2 + 0.1d2 = 0.0
-0.6 + -0.5d + 0.1d2 = 0.0

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

Divide each side by '0.1'.
-6 + -5d + d2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -5d + 6 + d2 = 0 + 6

Reorder the terms:
-6 + 6 + -5d + d2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5d + d2 = 0 + 6
-5d + d2 = 0 + 6

Combine like terms: 0 + 6 = 6
-5d + d2 = 6

The d term is -5d.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5d + 6.25 + d2 = 6 + 6.25

Reorder the terms:
6.25 + -5d + d2 = 6 + 6.25

Combine like terms: 6 + 6.25 = 12.25
6.25 + -5d + d2 = 12.25

Factor a perfect square on the left side:
(d + -2.5)(d + -2.5) = 12.25

Calculate the square root of the right side: 3.5

Break this problem into two subproblems by setting 
(d + -2.5) equal to 3.5 and -3.5.

Subproblem 1
d + -2.5 = 3.5

Simplifying
d + -2.5 = 3.5

Reorder the terms:
-2.5 + d = 3.5

Solving
-2.5 + d = 3.5

Solving for variable 'd'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + d = 3.5 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + d = 3.5 + 2.5
d = 3.5 + 2.5

Combine like terms: 3.5 + 2.5 = 6
d = 6

Simplifying
d = 6

Subproblem 2
d + -2.5 = -3.5

Simplifying
d + -2.5 = -3.5

Reorder the terms:
-2.5 + d = -3.5

Solving
-2.5 + d = -3.5

Solving for variable 'd'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + d = -3.5 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + d = -3.5 + 2.5
d = -3.5 + 2.5

Combine like terms: -3.5 + 2.5 = -1
d = -1

Simplifying
d = -1

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {6, -1}