1.5x^2+4.5x-2000=0

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Solution for 1.5x^2+4.5x-2000=0 equation: 


Simplifying
1.5x2 + 4.5x + -2000 = 0

Reorder the terms:
-2000 + 4.5x + 1.5x2 = 0

Solving
-2000 + 4.5x + 1.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '1.5'.
-1333.333333 + 3x + x2 = 0

Move the constant term to the right:

Add '1333.333333' to each side of the equation.
-1333.333333 + 3x + 1333.333333 + x2 = 0 + 1333.333333

Reorder the terms:
-1333.333333 + 1333.333333 + 3x + x2 = 0 + 1333.333333

Combine like terms: -1333.333333 + 1333.333333 = 0.000000
0.000000 + 3x + x2 = 0 + 1333.333333
3x + x2 = 0 + 1333.333333

Combine like terms: 0 + 1333.333333 = 1333.333333
3x + x2 = 1333.333333

The x term is 3x.  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.
3x + 2.25 + x2 = 1333.333333 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 1333.333333 + 2.25

Combine like terms: 1333.333333 + 2.25 = 1335.583333
2.25 + 3x + x2 = 1335.583333

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 1335.583333

Calculate the square root of the right side: 36.54563357

Break this problem into two subproblems by setting 
(x + 1.5) equal to 36.54563357 and -36.54563357.


Subproblem 1
x + 1.5 = 36.54563357

Simplifying
x + 1.5 = 36.54563357

Reorder the terms:
1.5 + x = 36.54563357

Solving
1.5 + x = 36.54563357

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 36.54563357 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 36.54563357 + -1.5
x = 36.54563357 + -1.5

Combine like terms: 36.54563357 + -1.5 = 35.04563357
x = 35.04563357

Simplifying
x = 35.04563357


Subproblem 2
x + 1.5 = -36.54563357

Simplifying
x + 1.5 = -36.54563357

Reorder the terms:
1.5 + x = -36.54563357

Solving
1.5 + x = -36.54563357

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -36.54563357 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -36.54563357 + -1.5
x = -36.54563357 + -1.5

Combine like terms: -36.54563357 + -1.5 = -38.04563357
x = -38.04563357

Simplifying
x = -38.04563357


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.04563357, -38.04563357}

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