d^2-5d=3d^2+1

Solution for d^2-5d=3d^2+1 equation:

Simplifying
d2 + -5d = 3d2 + 1

Reorder the terms:
-5d + d2 = 3d2 + 1

Reorder the terms:
-5d + d2 = 1 + 3d2

Solving
-5d + d2 = 1 + 3d2

Solving for variable 'd'.

Reorder the terms:
-1 + -5d + d2 + -3d2 = 1 + 3d2 + -1 + -3d2

Combine like terms: d2 + -3d2 = -2d2
-1 + -5d + -2d2 = 1 + 3d2 + -1 + -3d2

Reorder the terms:
-1 + -5d + -2d2 = 1 + -1 + 3d2 + -3d2

Combine like terms: 1 + -1 = 0
-1 + -5d + -2d2 = 0 + 3d2 + -3d2
-1 + -5d + -2d2 = 3d2 + -3d2

Combine like terms: 3d2 + -3d2 = 0
-1 + -5d + -2d2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 5d + 2d2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 5d + 2d2)' equal to zero and attempt to solve:

Simplifying
1 + 5d + 2d2 = 0

Solving
1 + 5d + 2d2 = 0

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

Divide each side by '2'.
0.5 + 2.5d + d2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 2.5d + -0.5 + d2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 2.5d + d2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 2.5d + d2 = 0 + -0.5
2.5d + d2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
2.5d + d2 = -0.5

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 = -0.5 + 1.5625

Reorder the terms:
1.5625 + 2.5d + d2 = -0.5 + 1.5625

Combine like terms: -0.5 + 1.5625 = 1.0625
1.5625 + 2.5d + d2 = 1.0625

Factor a perfect square on the left side:
(d + 1.25)(d + 1.25) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(d + 1.25) equal to 1.030776406 and -1.030776406.

Subproblem 1
d + 1.25 = 1.030776406

Simplifying
d + 1.25 = 1.030776406

Reorder the terms:
1.25 + d = 1.030776406

Solving
1.25 + d = 1.030776406

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 = 1.030776406 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + d = 1.030776406 + -1.25
d = 1.030776406 + -1.25

Combine like terms: 1.030776406 + -1.25 = -0.219223594
d = -0.219223594

Simplifying
d = -0.219223594

Subproblem 2
d + 1.25 = -1.030776406

Simplifying
d + 1.25 = -1.030776406

Reorder the terms:
1.25 + d = -1.030776406

Solving
1.25 + d = -1.030776406

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 = -1.030776406 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + d = -1.030776406 + -1.25
d = -1.030776406 + -1.25

Combine like terms: -1.030776406 + -1.25 = -2.280776406
d = -2.280776406

Simplifying
d = -2.280776406

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {-0.219223594, -2.280776406}
Solution
d = {-0.219223594, -2.280776406}