3d^2-4d-3=0

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Solution for 3d^2-4d-3=0 equation:


Simplifying
3d2 + -4d + -3 = 0

Reorder the terms:
-3 + -4d + 3d2 = 0

Solving
-3 + -4d + 3d2 = 0

Solving for variable 'd'.

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

Divide each side by '3'.
-1 + -1.333333333d + d2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.333333333d + 1 + d2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.333333333d + d2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.333333333d + d2 = 0 + 1
-1.333333333d + d2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.333333333d + d2 = 1

The d term is -1.333333333d.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333d + 0.4444444442 + d2 = 1 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333d + d2 = 1 + 0.4444444442

Combine like terms: 1 + 0.4444444442 = 1.4444444442
0.4444444442 + -1.333333333d + d2 = 1.4444444442

Factor a perfect square on the left side:
(d + -0.6666666665)(d + -0.6666666665) = 1.4444444442

Calculate the square root of the right side: 1.201850425

Break this problem into two subproblems by setting 
(d + -0.6666666665) equal to 1.201850425 and -1.201850425.

Subproblem 1

d + -0.6666666665 = 1.201850425 Simplifying d + -0.6666666665 = 1.201850425 Reorder the terms: -0.6666666665 + d = 1.201850425 Solving -0.6666666665 + d = 1.201850425 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + d = 1.201850425 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + d = 1.201850425 + 0.6666666665 d = 1.201850425 + 0.6666666665 Combine like terms: 1.201850425 + 0.6666666665 = 1.8685170915 d = 1.8685170915 Simplifying d = 1.8685170915

Subproblem 2

d + -0.6666666665 = -1.201850425 Simplifying d + -0.6666666665 = -1.201850425 Reorder the terms: -0.6666666665 + d = -1.201850425 Solving -0.6666666665 + d = -1.201850425 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + d = -1.201850425 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + d = -1.201850425 + 0.6666666665 d = -1.201850425 + 0.6666666665 Combine like terms: -1.201850425 + 0.6666666665 = -0.5351837585 d = -0.5351837585 Simplifying d = -0.5351837585

Solution

The solution to the problem is based on the solutions from the subproblems. d = {1.8685170915, -0.5351837585}

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