15d^2-48d+9=1

Solution for 15d^2-48d+9=1 equation:

Simplifying
15d2 + -48d + 9 = 1

Reorder the terms:
9 + -48d + 15d2 = 1

Solving
9 + -48d + 15d2 = 1

Solving for variable 'd'.

Reorder the terms:
9 + -1 + -48d + 15d2 = 1 + -1

Combine like terms: 9 + -1 = 8
8 + -48d + 15d2 = 1 + -1

Combine like terms: 1 + -1 = 0
8 + -48d + 15d2 = 0

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

Divide each side by '15'.
0.5333333333 + -3.2d + d2 = 0

Move the constant term to the right:

Add '-0.5333333333' to each side of the equation.
0.5333333333 + -3.2d + -0.5333333333 + d2 = 0 + -0.5333333333

Reorder the terms:
0.5333333333 + -0.5333333333 + -3.2d + d2 = 0 + -0.5333333333

Combine like terms: 0.5333333333 + -0.5333333333 = 0.0000000000
0.0000000000 + -3.2d + d2 = 0 + -0.5333333333
-3.2d + d2 = 0 + -0.5333333333

Combine like terms: 0 + -0.5333333333 = -0.5333333333
-3.2d + d2 = -0.5333333333

The d term is -3.2d.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2d + 2.56 + d2 = -0.5333333333 + 2.56

Reorder the terms:
2.56 + -3.2d + d2 = -0.5333333333 + 2.56

Combine like terms: -0.5333333333 + 2.56 = 2.0266666667
2.56 + -3.2d + d2 = 2.0266666667

Factor a perfect square on the left side:
(d + -1.6)(d + -1.6) = 2.0266666667

Calculate the square root of the right side: 1.423610434

Break this problem into two subproblems by setting 
(d + -1.6) equal to 1.423610434 and -1.423610434.

Subproblem 1
d + -1.6 = 1.423610434

Simplifying
d + -1.6 = 1.423610434

Reorder the terms:
-1.6 + d = 1.423610434

Solving
-1.6 + d = 1.423610434

Solving for variable 'd'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + d = 1.423610434 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + d = 1.423610434 + 1.6
d = 1.423610434 + 1.6

Combine like terms: 1.423610434 + 1.6 = 3.023610434
d = 3.023610434

Simplifying
d = 3.023610434

Subproblem 2
d + -1.6 = -1.423610434

Simplifying
d + -1.6 = -1.423610434

Reorder the terms:
-1.6 + d = -1.423610434

Solving
-1.6 + d = -1.423610434

Solving for variable 'd'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + d = -1.423610434 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + d = -1.423610434 + 1.6
d = -1.423610434 + 1.6

Combine like terms: -1.423610434 + 1.6 = 0.176389566
d = 0.176389566

Simplifying
d = 0.176389566

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {3.023610434, 0.176389566}