(0.75d^2)-0.9*d-1.5=0

Solution for (0.75d^2)-0.9*d-1.5=0 equation:

Simplifying
(0.75d2) + -0.9d + -1.5 = 0

Reorder the terms:
-1.5 + -0.9d + (0.75d2) = 0

Solving
-1.5 + -0.9d + (0.75d2) = 0

Solving for variable 'd'.

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

Divide each side by '0.75'.
-2 + -1.2d + d2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -1.2d + 2 + d2 = 0 + 2

Reorder the terms:
-2 + 2 + -1.2d + d2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1.2d + d2 = 0 + 2
-1.2d + d2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1.2d + d2 = 2

The d term is -1.2d.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2d + 0.36 + d2 = 2 + 0.36

Reorder the terms:
0.36 + -1.2d + d2 = 2 + 0.36

Combine like terms: 2 + 0.36 = 2.36
0.36 + -1.2d + d2 = 2.36

Factor a perfect square on the left side:
((d) + -0.6)((d) + -0.6) = 2.36

Calculate the square root of the right side: 1.53622915

Break this problem into two subproblems by setting 
((d) + -0.6) equal to 1.53622915 and -1.53622915.

Subproblem 1
(d) + -0.6 = 1.53622915

Simplifying
(d) + -0.6 = 1.53622915
d + -0.6 = 1.53622915

Reorder the terms:
-0.6 + d = 1.53622915

Solving
-0.6 + d = 1.53622915

Solving for variable 'd'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + d = 1.53622915 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + d = 1.53622915 + 0.6
d = 1.53622915 + 0.6

Combine like terms: 1.53622915 + 0.6 = 2.13622915
d = 2.13622915

Simplifying
d = 2.13622915

Subproblem 2
(d) + -0.6 = -1.53622915

Simplifying
(d) + -0.6 = -1.53622915
d + -0.6 = -1.53622915

Reorder the terms:
-0.6 + d = -1.53622915

Solving
-0.6 + d = -1.53622915

Solving for variable 'd'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + d = -1.53622915 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + d = -1.53622915 + 0.6
d = -1.53622915 + 0.6

Combine like terms: -1.53622915 + 0.6 = -0.93622915
d = -0.93622915

Simplifying
d = -0.93622915

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {2.13622915, -0.93622915}