3x^2-4x-201=0

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Solution for 3x^2-4x-201=0 equation: 


Simplifying
3x2 + -4x + -201 = 0

Reorder the terms:
-201 + -4x + 3x2 = 0

Solving
-201 + -4x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-67 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '67' to each side of the equation.
-67 + -1.333333333x + 67 + x2 = 0 + 67

Reorder the terms:
-67 + 67 + -1.333333333x + x2 = 0 + 67

Combine like terms: -67 + 67 = 0
0 + -1.333333333x + x2 = 0 + 67
-1.333333333x + x2 = 0 + 67

Combine like terms: 0 + 67 = 67
-1.333333333x + x2 = 67

The x term is -1.333333333x.  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.
-1.333333333x + 0.4444444442 + x2 = 67 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 67 + 0.4444444442

Combine like terms: 67 + 0.4444444442 = 67.4444444442
0.4444444442 + -1.333333333x + x2 = 67.4444444442

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 67.4444444442

Calculate the square root of the right side: 8.212456663

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 8.212456663 and -8.212456663.


Subproblem 1
x + -0.6666666665 = 8.212456663

Simplifying
x + -0.6666666665 = 8.212456663

Reorder the terms:
-0.6666666665 + x = 8.212456663

Solving
-0.6666666665 + x = 8.212456663

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 8.212456663 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 8.212456663 + 0.6666666665
x = 8.212456663 + 0.6666666665

Combine like terms: 8.212456663 + 0.6666666665 = 8.8791233295
x = 8.8791233295

Simplifying
x = 8.8791233295


Subproblem 2
x + -0.6666666665 = -8.212456663

Simplifying
x + -0.6666666665 = -8.212456663

Reorder the terms:
-0.6666666665 + x = -8.212456663

Solving
-0.6666666665 + x = -8.212456663

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -8.212456663 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -8.212456663 + 0.6666666665
x = -8.212456663 + 0.6666666665

Combine like terms: -8.212456663 + 0.6666666665 = -7.5457899965
x = -7.5457899965

Simplifying
x = -7.5457899965


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.8791233295, -7.5457899965}

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