1.5x^2+x-2.5=0

Solution for 1.5x^2+x-2.5=0 equation:

Simplifying
1.5x2 + x + -2.5 = 0

Reorder the terms:
-2.5 + x + 1.5x2 = 0

Solving
-2.5 + x + 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'.
-1.666666667 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 0.6666666667x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 0.6666666667x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 0.6666666667x + x2 = 0 + 1.666666667
0.6666666667x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
0.6666666667x + x2 = 1.666666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.6666666667x + 0.25 + x2 = 1.666666667 + 0.25

Reorder the terms:
0.25 + 0.6666666667x + x2 = 1.666666667 + 0.25

Combine like terms: 1.666666667 + 0.25 = 1.916666667
0.25 + 0.6666666667x + x2 = 1.916666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.916666667

Calculate the square root of the right side: 1.384437311

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.384437311 and -1.384437311.

Subproblem 1
x + 0.5 = 1.384437311

Simplifying
x + 0.5 = 1.384437311

Reorder the terms:
0.5 + x = 1.384437311

Solving
0.5 + x = 1.384437311

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.384437311 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.384437311 + -0.5
x = 1.384437311 + -0.5

Combine like terms: 1.384437311 + -0.5 = 0.884437311
x = 0.884437311

Simplifying
x = 0.884437311

Subproblem 2
x + 0.5 = -1.384437311

Simplifying
x + 0.5 = -1.384437311

Reorder the terms:
0.5 + x = -1.384437311

Solving
0.5 + x = -1.384437311

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.384437311 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.384437311 + -0.5
x = -1.384437311 + -0.5

Combine like terms: -1.384437311 + -0.5 = -1.884437311
x = -1.884437311

Simplifying
x = -1.884437311

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.884437311, -1.884437311}