7n^2+3n=11

Solution for 7n^2+3n=11 equation:

Simplifying
7n2 + 3n = 11

Reorder the terms:
3n + 7n2 = 11

Solving
3n + 7n2 = 11

Solving for variable 'n'.

Reorder the terms:
-11 + 3n + 7n2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + 3n + 7n2 = 0

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

Divide each side by '7'.
-1.571428571 + 0.4285714286n + n2 = 0

Move the constant term to the right:

Add '1.571428571' to each side of the equation.
-1.571428571 + 0.4285714286n + 1.571428571 + n2 = 0 + 1.571428571

Reorder the terms:
-1.571428571 + 1.571428571 + 0.4285714286n + n2 = 0 + 1.571428571

Combine like terms: -1.571428571 + 1.571428571 = 0.000000000
0.000000000 + 0.4285714286n + n2 = 0 + 1.571428571
0.4285714286n + n2 = 0 + 1.571428571

Combine like terms: 0 + 1.571428571 = 1.571428571
0.4285714286n + n2 = 1.571428571

The n term is 0.4285714286n.  Take half its coefficient (0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
0.4285714286n + 0.04591836735 + n2 = 1.571428571 + 0.04591836735

Reorder the terms:
0.04591836735 + 0.4285714286n + n2 = 1.571428571 + 0.04591836735

Combine like terms: 1.571428571 + 0.04591836735 = 1.61734693835
0.04591836735 + 0.4285714286n + n2 = 1.61734693835

Factor a perfect square on the left side:
(n + 0.2142857143)(n + 0.2142857143) = 1.61734693835

Calculate the square root of the right side: 1.271749558

Break this problem into two subproblems by setting 
(n + 0.2142857143) equal to 1.271749558 and -1.271749558.

Subproblem 1
n + 0.2142857143 = 1.271749558

Simplifying
n + 0.2142857143 = 1.271749558

Reorder the terms:
0.2142857143 + n = 1.271749558

Solving
0.2142857143 + n = 1.271749558

Solving for variable 'n'.

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

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.2142857143 + n = 1.271749558 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + n = 1.271749558 + -0.2142857143
n = 1.271749558 + -0.2142857143

Combine like terms: 1.271749558 + -0.2142857143 = 1.0574638437
n = 1.0574638437

Simplifying
n = 1.0574638437

Subproblem 2
n + 0.2142857143 = -1.271749558

Simplifying
n + 0.2142857143 = -1.271749558

Reorder the terms:
0.2142857143 + n = -1.271749558

Solving
0.2142857143 + n = -1.271749558

Solving for variable 'n'.

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

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.2142857143 + n = -1.271749558 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + n = -1.271749558 + -0.2142857143
n = -1.271749558 + -0.2142857143

Combine like terms: -1.271749558 + -0.2142857143 = -1.4860352723
n = -1.4860352723

Simplifying
n = -1.4860352723

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.0574638437, -1.4860352723}