6n^2-5n-1400=0

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Solution for 6n^2-5n-1400=0 equation: 


Simplifying
6n2 + -5n + -1400 = 0

Reorder the terms:
-1400 + -5n + 6n2 = 0

Solving
-1400 + -5n + 6n2 = 0

Solving for variable 'n'.

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

Divide each side by '6'.
-233.3333333 + -0.8333333333n + n2 = 0

Move the constant term to the right:

Add '233.3333333' to each side of the equation.
-233.3333333 + -0.8333333333n + 233.3333333 + n2 = 0 + 233.3333333

Reorder the terms:
-233.3333333 + 233.3333333 + -0.8333333333n + n2 = 0 + 233.3333333

Combine like terms: -233.3333333 + 233.3333333 = 0.0000000
0.0000000 + -0.8333333333n + n2 = 0 + 233.3333333
-0.8333333333n + n2 = 0 + 233.3333333

Combine like terms: 0 + 233.3333333 = 233.3333333
-0.8333333333n + n2 = 233.3333333

The n term is -0.8333333333n.  Take half its coefficient (-0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
-0.8333333333n + 0.1736111111 + n2 = 233.3333333 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333n + n2 = 233.3333333 + 0.1736111111

Combine like terms: 233.3333333 + 0.1736111111 = 233.5069444111
0.1736111111 + -0.8333333333n + n2 = 233.5069444111

Factor a perfect square on the left side:
(n + -0.4166666667)(n + -0.4166666667) = 233.5069444111

Calculate the square root of the right side: 15.280934016

Break this problem into two subproblems by setting 
(n + -0.4166666667) equal to 15.280934016 and -15.280934016.


Subproblem 1
n + -0.4166666667 = 15.280934016

Simplifying
n + -0.4166666667 = 15.280934016

Reorder the terms:
-0.4166666667 + n = 15.280934016

Solving
-0.4166666667 + n = 15.280934016

Solving for variable 'n'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + n = 15.280934016 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + n = 15.280934016 + 0.4166666667
n = 15.280934016 + 0.4166666667

Combine like terms: 15.280934016 + 0.4166666667 = 15.6976006827
n = 15.6976006827

Simplifying
n = 15.6976006827


Subproblem 2
n + -0.4166666667 = -15.280934016

Simplifying
n + -0.4166666667 = -15.280934016

Reorder the terms:
-0.4166666667 + n = -15.280934016

Solving
-0.4166666667 + n = -15.280934016

Solving for variable 'n'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + n = -15.280934016 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + n = -15.280934016 + 0.4166666667
n = -15.280934016 + 0.4166666667

Combine like terms: -15.280934016 + 0.4166666667 = -14.8642673493
n = -14.8642673493

Simplifying
n = -14.8642673493


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {15.6976006827, -14.8642673493}

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