0.3x^2+1.8x+2.4=0

Solution for 0.3x^2+1.8x+2.4=0 equation:

Simplifying
0.3x2 + 1.8x + 2.4 = 0

Reorder the terms:
2.4 + 1.8x + 0.3x2 = 0

Solving
2.4 + 1.8x + 0.3x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.3'.
8 + 6x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 6x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 6x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 6x + x2 = 0 + -8
6x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
6x + x2 = -8

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -8 + 9

Reorder the terms:
9 + 6x + x2 = -8 + 9

Combine like terms: -8 + 9 = 1
9 + 6x + x2 = 1

Factor a perfect square on the left side:
(x + 3)(x + 3) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + 3) equal to 1 and -1.

Subproblem 1
x + 3 = 1

Simplifying
x + 3 = 1

Reorder the terms:
3 + x = 1

Solving
3 + x = 1

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 1 + -3

Combine like terms: 3 + -3 = 0
0 + x = 1 + -3
x = 1 + -3

Combine like terms: 1 + -3 = -2
x = -2

Simplifying
x = -2

Subproblem 2
x + 3 = -1

Simplifying
x + 3 = -1

Reorder the terms:
3 + x = -1

Solving
3 + x = -1

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -1 + -3

Combine like terms: 3 + -3 = 0
0 + x = -1 + -3
x = -1 + -3

Combine like terms: -1 + -3 = -4
x = -4

Simplifying
x = -4

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2, -4}