2l^2-3l-146=0

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Solution for 2l^2-3l-146=0 equation: 


Simplifying
2l2 + -3l + -146 = 0

Reorder the terms:
-146 + -3l + 2l2 = 0

Solving
-146 + -3l + 2l2 = 0

Solving for variable 'l'.

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

Divide each side by '2'.
-73 + -1.5l + l2 = 0

Move the constant term to the right:

Add '73' to each side of the equation.
-73 + -1.5l + 73 + l2 = 0 + 73

Reorder the terms:
-73 + 73 + -1.5l + l2 = 0 + 73

Combine like terms: -73 + 73 = 0
0 + -1.5l + l2 = 0 + 73
-1.5l + l2 = 0 + 73

Combine like terms: 0 + 73 = 73
-1.5l + l2 = 73

The l term is -1.5l.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5l + 0.5625 + l2 = 73 + 0.5625

Reorder the terms:
0.5625 + -1.5l + l2 = 73 + 0.5625

Combine like terms: 73 + 0.5625 = 73.5625
0.5625 + -1.5l + l2 = 73.5625

Factor a perfect square on the left side:
(l + -0.75)(l + -0.75) = 73.5625

Calculate the square root of the right side: 8.576858399

Break this problem into two subproblems by setting 
(l + -0.75) equal to 8.576858399 and -8.576858399.


Subproblem 1
l + -0.75 = 8.576858399

Simplifying
l + -0.75 = 8.576858399

Reorder the terms:
-0.75 + l = 8.576858399

Solving
-0.75 + l = 8.576858399

Solving for variable 'l'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + l = 8.576858399 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + l = 8.576858399 + 0.75
l = 8.576858399 + 0.75

Combine like terms: 8.576858399 + 0.75 = 9.326858399
l = 9.326858399

Simplifying
l = 9.326858399


Subproblem 2
l + -0.75 = -8.576858399

Simplifying
l + -0.75 = -8.576858399

Reorder the terms:
-0.75 + l = -8.576858399

Solving
-0.75 + l = -8.576858399

Solving for variable 'l'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + l = -8.576858399 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + l = -8.576858399 + 0.75
l = -8.576858399 + 0.75

Combine like terms: -8.576858399 + 0.75 = -7.826858399
l = -7.826858399

Simplifying
l = -7.826858399


Solution
The solution to the problem is based on the solutions
from the subproblems.
l = {9.326858399, -7.826858399}

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