1800=2n^2-18n

Solution for 1800=2n^2-18n equation:

Simplifying
1800 = 2n2 + -18n

Reorder the terms:
1800 = -18n + 2n2

Solving
1800 = -18n + 2n2

Solving for variable 'n'.

Reorder the terms:
1800 + 18n + -2n2 = -18n + 18n + 2n2 + -2n2

Combine like terms: -18n + 18n = 0
1800 + 18n + -2n2 = 0 + 2n2 + -2n2
1800 + 18n + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
1800 + 18n + -2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(900 + 9n + -1n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(900 + 9n + -1n2)' equal to zero and attempt to solve:

Simplifying
900 + 9n + -1n2 = 0

Solving
900 + 9n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-900 + -9n + n2 = 0

Move the constant term to the right:

Add '900' to each side of the equation.
-900 + -9n + 900 + n2 = 0 + 900

Reorder the terms:
-900 + 900 + -9n + n2 = 0 + 900

Combine like terms: -900 + 900 = 0
0 + -9n + n2 = 0 + 900
-9n + n2 = 0 + 900

Combine like terms: 0 + 900 = 900
-9n + n2 = 900

The n term is -9n.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9n + 20.25 + n2 = 900 + 20.25

Reorder the terms:
20.25 + -9n + n2 = 900 + 20.25

Combine like terms: 900 + 20.25 = 920.25
20.25 + -9n + n2 = 920.25

Factor a perfect square on the left side:
(n + -4.5)(n + -4.5) = 920.25

Calculate the square root of the right side: 30.335622624

Break this problem into two subproblems by setting 
(n + -4.5) equal to 30.335622624 and -30.335622624.

Subproblem 1
n + -4.5 = 30.335622624

Simplifying
n + -4.5 = 30.335622624

Reorder the terms:
-4.5 + n = 30.335622624

Solving
-4.5 + n = 30.335622624

Solving for variable 'n'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + n = 30.335622624 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + n = 30.335622624 + 4.5
n = 30.335622624 + 4.5

Combine like terms: 30.335622624 + 4.5 = 34.835622624
n = 34.835622624

Simplifying
n = 34.835622624

Subproblem 2
n + -4.5 = -30.335622624

Simplifying
n + -4.5 = -30.335622624

Reorder the terms:
-4.5 + n = -30.335622624

Solving
-4.5 + n = -30.335622624

Solving for variable 'n'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + n = -30.335622624 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + n = -30.335622624 + 4.5
n = -30.335622624 + 4.5

Combine like terms: -30.335622624 + 4.5 = -25.835622624
n = -25.835622624

Simplifying
n = -25.835622624

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {34.835622624, -25.835622624}
Solution
n = {34.835622624, -25.835622624}