-1.5x^2-7.5x+45.9=0

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Solution for -1.5x^2-7.5x+45.9=0 equation: 


Simplifying
-1.5x2 + -7.5x + 45.9 = 0

Reorder the terms:
45.9 + -7.5x + -1.5x2 = 0

Solving
45.9 + -7.5x + -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'.
-30.6 + 5x + x2 = 0

Move the constant term to the right:

Add '30.6' to each side of the equation.
-30.6 + 5x + 30.6 + x2 = 0 + 30.6

Reorder the terms:
-30.6 + 30.6 + 5x + x2 = 0 + 30.6

Combine like terms: -30.6 + 30.6 = 0.0
0.0 + 5x + x2 = 0 + 30.6
5x + x2 = 0 + 30.6

Combine like terms: 0 + 30.6 = 30.6
5x + x2 = 30.6

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 30.6 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 30.6 + 6.25

Combine like terms: 30.6 + 6.25 = 36.85
6.25 + 5x + x2 = 36.85

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 36.85

Calculate the square root of the right side: 6.070420084

Break this problem into two subproblems by setting 
(x + 2.5) equal to 6.070420084 and -6.070420084.


Subproblem 1
x + 2.5 = 6.070420084

Simplifying
x + 2.5 = 6.070420084

Reorder the terms:
2.5 + x = 6.070420084

Solving
2.5 + x = 6.070420084

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 6.070420084 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 6.070420084 + -2.5
x = 6.070420084 + -2.5

Combine like terms: 6.070420084 + -2.5 = 3.570420084
x = 3.570420084

Simplifying
x = 3.570420084


Subproblem 2
x + 2.5 = -6.070420084

Simplifying
x + 2.5 = -6.070420084

Reorder the terms:
2.5 + x = -6.070420084

Solving
2.5 + x = -6.070420084

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -6.070420084 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -6.070420084 + -2.5
x = -6.070420084 + -2.5

Combine like terms: -6.070420084 + -2.5 = -8.570420084
x = -8.570420084

Simplifying
x = -8.570420084


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.570420084, -8.570420084}

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