L^2-2L-20=0

Solution for L^2-2L-20=0 equation:

Simplifying
L2 + -2L + -20 = 0

Reorder the terms:
-20 + -2L + L2 = 0

Solving
-20 + -2L + L2 = 0

Solving for variable 'L'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -2L + 20 + L2 = 0 + 20

Reorder the terms:
-20 + 20 + -2L + L2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -2L + L2 = 0 + 20
-2L + L2 = 0 + 20

Combine like terms: 0 + 20 = 20
-2L + L2 = 20

The L term is -2L.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2L + 1 + L2 = 20 + 1

Reorder the terms:
1 + -2L + L2 = 20 + 1

Combine like terms: 20 + 1 = 21
1 + -2L + L2 = 21

Factor a perfect square on the left side:
(L + -1)(L + -1) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(L + -1) equal to 4.582575695 and -4.582575695.

Subproblem 1
L + -1 = 4.582575695

Simplifying
L + -1 = 4.582575695

Reorder the terms:
-1 + L = 4.582575695

Solving
-1 + L = 4.582575695

Solving for variable 'L'.

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

Add '1' to each side of the equation.
-1 + 1 + L = 4.582575695 + 1

Combine like terms: -1 + 1 = 0
0 + L = 4.582575695 + 1
L = 4.582575695 + 1

Combine like terms: 4.582575695 + 1 = 5.582575695
L = 5.582575695

Simplifying
L = 5.582575695

Subproblem 2
L + -1 = -4.582575695

Simplifying
L + -1 = -4.582575695

Reorder the terms:
-1 + L = -4.582575695

Solving
-1 + L = -4.582575695

Solving for variable 'L'.

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

Add '1' to each side of the equation.
-1 + 1 + L = -4.582575695 + 1

Combine like terms: -1 + 1 = 0
0 + L = -4.582575695 + 1
L = -4.582575695 + 1

Combine like terms: -4.582575695 + 1 = -3.582575695
L = -3.582575695

Simplifying
L = -3.582575695

Solution
The solution to the problem is based on the solutions
from the subproblems.
L = {5.582575695, -3.582575695}