3x^2-8x-960=0

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Solution for 3x^2-8x-960=0 equation: 


Simplifying
3x2 + -8x + -960 = 0

Reorder the terms:
-960 + -8x + 3x2 = 0

Solving
-960 + -8x + 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'.
-320 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '320' to each side of the equation.
-320 + -2.666666667x + 320 + x2 = 0 + 320

Reorder the terms:
-320 + 320 + -2.666666667x + x2 = 0 + 320

Combine like terms: -320 + 320 = 0
0 + -2.666666667x + x2 = 0 + 320
-2.666666667x + x2 = 0 + 320

Combine like terms: 0 + 320 = 320
-2.666666667x + x2 = 320

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 320 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 320 + 1.777777780

Combine like terms: 320 + 1.777777780 = 321.77777778
1.777777780 + -2.666666667x + x2 = 321.77777778

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 321.77777778

Calculate the square root of the right side: 17.938165396

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 17.938165396 and -17.938165396.


Subproblem 1
x + -1.333333334 = 17.938165396

Simplifying
x + -1.333333334 = 17.938165396

Reorder the terms:
-1.333333334 + x = 17.938165396

Solving
-1.333333334 + x = 17.938165396

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 17.938165396 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 17.938165396 + 1.333333334
x = 17.938165396 + 1.333333334

Combine like terms: 17.938165396 + 1.333333334 = 19.27149873
x = 19.27149873

Simplifying
x = 19.27149873


Subproblem 2
x + -1.333333334 = -17.938165396

Simplifying
x + -1.333333334 = -17.938165396

Reorder the terms:
-1.333333334 + x = -17.938165396

Solving
-1.333333334 + x = -17.938165396

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -17.938165396 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -17.938165396 + 1.333333334
x = -17.938165396 + 1.333333334

Combine like terms: -17.938165396 + 1.333333334 = -16.604832062
x = -16.604832062

Simplifying
x = -16.604832062


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.27149873, -16.604832062}

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