n^2-3n-80=0

Solution for n^2-3n-80=0 equation:

Simplifying
n2 + -3n + -80 = 0

Reorder the terms:
-80 + -3n + n2 = 0

Solving
-80 + -3n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -3n + 80 + n2 = 0 + 80

Reorder the terms:
-80 + 80 + -3n + n2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -3n + n2 = 0 + 80
-3n + n2 = 0 + 80

Combine like terms: 0 + 80 = 80
-3n + n2 = 80

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = 80 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 80 + 2.25

Combine like terms: 80 + 2.25 = 82.25
2.25 + -3n + n2 = 82.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 82.25

Calculate the square root of the right side: 9.069178574

Break this problem into two subproblems by setting 
(n + -1.5) equal to 9.069178574 and -9.069178574.

Subproblem 1
n + -1.5 = 9.069178574

Simplifying
n + -1.5 = 9.069178574

Reorder the terms:
-1.5 + n = 9.069178574

Solving
-1.5 + n = 9.069178574

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = 9.069178574 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 9.069178574 + 1.5
n = 9.069178574 + 1.5

Combine like terms: 9.069178574 + 1.5 = 10.569178574
n = 10.569178574

Simplifying
n = 10.569178574

Subproblem 2
n + -1.5 = -9.069178574

Simplifying
n + -1.5 = -9.069178574

Reorder the terms:
-1.5 + n = -9.069178574

Solving
-1.5 + n = -9.069178574

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = -9.069178574 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -9.069178574 + 1.5
n = -9.069178574 + 1.5

Combine like terms: -9.069178574 + 1.5 = -7.569178574
n = -7.569178574

Simplifying
n = -7.569178574

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {10.569178574, -7.569178574}