3n^2+17n-4000=0

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Solution for 3n^2+17n-4000=0 equation: 


Simplifying
3n2 + 17n + -4000 = 0

Reorder the terms:
-4000 + 17n + 3n2 = 0

Solving
-4000 + 17n + 3n2 = 0

Solving for variable 'n'.

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

Divide each side by '3'.
-1333.333333 + 5.666666667n + n2 = 0

Move the constant term to the right:

Add '1333.333333' to each side of the equation.
-1333.333333 + 5.666666667n + 1333.333333 + n2 = 0 + 1333.333333

Reorder the terms:
-1333.333333 + 1333.333333 + 5.666666667n + n2 = 0 + 1333.333333

Combine like terms: -1333.333333 + 1333.333333 = 0.000000
0.000000 + 5.666666667n + n2 = 0 + 1333.333333
5.666666667n + n2 = 0 + 1333.333333

Combine like terms: 0 + 1333.333333 = 1333.333333
5.666666667n + n2 = 1333.333333

The n term is 5.666666667n.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667n + 8.027777782 + n2 = 1333.333333 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667n + n2 = 1333.333333 + 8.027777782

Combine like terms: 1333.333333 + 8.027777782 = 1341.361110782
8.027777782 + 5.666666667n + n2 = 1341.361110782

Factor a perfect square on the left side:
(n + 2.833333334)(n + 2.833333334) = 1341.361110782

Calculate the square root of the right side: 36.624597073

Break this problem into two subproblems by setting 
(n + 2.833333334) equal to 36.624597073 and -36.624597073.


Subproblem 1
n + 2.833333334 = 36.624597073

Simplifying
n + 2.833333334 = 36.624597073

Reorder the terms:
2.833333334 + n = 36.624597073

Solving
2.833333334 + n = 36.624597073

Solving for variable 'n'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + n = 36.624597073 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + n = 36.624597073 + -2.833333334
n = 36.624597073 + -2.833333334

Combine like terms: 36.624597073 + -2.833333334 = 33.791263739
n = 33.791263739

Simplifying
n = 33.791263739


Subproblem 2
n + 2.833333334 = -36.624597073

Simplifying
n + 2.833333334 = -36.624597073

Reorder the terms:
2.833333334 + n = -36.624597073

Solving
2.833333334 + n = -36.624597073

Solving for variable 'n'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + n = -36.624597073 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + n = -36.624597073 + -2.833333334
n = -36.624597073 + -2.833333334

Combine like terms: -36.624597073 + -2.833333334 = -39.457930407
n = -39.457930407

Simplifying
n = -39.457930407


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {33.791263739, -39.457930407}

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