.5d^2-1.25d-3=0

Solution for .5d^2-1.25d-3=0 equation:

Simplifying
0.5d2 + -1.25d + -3 = 0

Reorder the terms:
-3 + -1.25d + 0.5d2 = 0

Solving
-3 + -1.25d + 0.5d2 = 0

Solving for variable 'd'.

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

Divide each side by '0.5'.
-6 + -2.5d + d2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2.5d + 6 + d2 = 0 + 6

Reorder the terms:
-6 + 6 + -2.5d + d2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2.5d + d2 = 0 + 6
-2.5d + d2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2.5d + d2 = 6

The d term is -2.5d.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5d + 1.5625 + d2 = 6 + 1.5625

Reorder the terms:
1.5625 + -2.5d + d2 = 6 + 1.5625

Combine like terms: 6 + 1.5625 = 7.5625
1.5625 + -2.5d + d2 = 7.5625

Factor a perfect square on the left side:
(d + -1.25)(d + -1.25) = 7.5625

Calculate the square root of the right side: 2.75

Break this problem into two subproblems by setting 
(d + -1.25) equal to 2.75 and -2.75.

Subproblem 1
d + -1.25 = 2.75

Simplifying
d + -1.25 = 2.75

Reorder the terms:
-1.25 + d = 2.75

Solving
-1.25 + d = 2.75

Solving for variable 'd'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + d = 2.75 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + d = 2.75 + 1.25
d = 2.75 + 1.25

Combine like terms: 2.75 + 1.25 = 4
d = 4

Simplifying
d = 4

Subproblem 2
d + -1.25 = -2.75

Simplifying
d + -1.25 = -2.75

Reorder the terms:
-1.25 + d = -2.75

Solving
-1.25 + d = -2.75

Solving for variable 'd'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + d = -2.75 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + d = -2.75 + 1.25
d = -2.75 + 1.25

Combine like terms: -2.75 + 1.25 = -1.5
d = -1.5

Simplifying
d = -1.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {4, -1.5}