1+2.4x+0.8x^2=0

Solution for 1+2.4x+0.8x^2=0 equation:

Simplifying
1 + 2.4x + 0.8x2 = 0

Solving
1 + 2.4x + 0.8x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.8'.
1.25 + 3x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + 3x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + 3x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + 3x + x2 = 0 + -1.25
3x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
3x + x2 = -1.25

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 = -1.25 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -1.25 + 2.25

Combine like terms: -1.25 + 2.25 = 1
2.25 + 3x + x2 = 1

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1 and -1.

Subproblem 1
x + 1.5 = 1

Simplifying
x + 1.5 = 1

Reorder the terms:
1.5 + x = 1

Solving
1.5 + x = 1

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 = 1 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1 + -1.5
x = 1 + -1.5

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

Simplifying
x = -0.5

Subproblem 2
x + 1.5 = -1

Simplifying
x + 1.5 = -1

Reorder the terms:
1.5 + x = -1

Solving
1.5 + x = -1

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 = -1 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1 + -1.5
x = -1 + -1.5

Combine like terms: -1 + -1.5 = -2.5
x = -2.5

Simplifying
x = -2.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.5, -2.5}