2x^2-4x+1.5=0

Solution for 2x^2-4x+1.5=0 equation:

Simplifying
2x2 + -4x + 1.5 = 0

Reorder the terms:
1.5 + -4x + 2x2 = 0

Solving
1.5 + -4x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
0.75 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -2x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -2x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -2x + x2 = 0 + -0.75
-2x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-2x + x2 = -0.75

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

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.75 + 1

Reorder the terms:
1 + -2x + x2 = -0.75 + 1

Combine like terms: -0.75 + 1 = 0.25
1 + -2x + x2 = 0.25

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.25

Calculate the square root of the right side: 0.5

Break this problem into two subproblems by setting 
(x + -1) equal to 0.5 and -0.5.

Subproblem 1
x + -1 = 0.5

Simplifying
x + -1 = 0.5

Reorder the terms:
-1 + x = 0.5

Solving
-1 + x = 0.5

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.5 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.5 + 1
x = 0.5 + 1

Combine like terms: 0.5 + 1 = 1.5
x = 1.5

Simplifying
x = 1.5

Subproblem 2
x + -1 = -0.5

Simplifying
x + -1 = -0.5

Reorder the terms:
-1 + x = -0.5

Solving
-1 + x = -0.5

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.5 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.5 + 1
x = -0.5 + 1

Combine like terms: -0.5 + 1 = 0.5
x = 0.5

Simplifying
x = 0.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5, 0.5}