0.3x^2-2.7x+2.4=0

Solution for 0.3x^2-2.7x+2.4=0 equation:

Simplifying
0.3x2 + -2.7x + 2.4 = 0

Reorder the terms:
2.4 + -2.7x + 0.3x2 = 0

Solving
2.4 + -2.7x + 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 + -9x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -9x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -9x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -9x + x2 = 0 + -8
-9x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-9x + x2 = -8

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -8 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -8 + 20.25

Combine like terms: -8 + 20.25 = 12.25
20.25 + -9x + x2 = 12.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 12.25

Calculate the square root of the right side: 3.5

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.5 and -3.5.

Subproblem 1
x + -4.5 = 3.5

Simplifying
x + -4.5 = 3.5

Reorder the terms:
-4.5 + x = 3.5

Solving
-4.5 + x = 3.5

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 3.5 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 3.5 + 4.5
x = 3.5 + 4.5

Combine like terms: 3.5 + 4.5 = 8
x = 8

Simplifying
x = 8

Subproblem 2
x + -4.5 = -3.5

Simplifying
x + -4.5 = -3.5

Reorder the terms:
-4.5 + x = -3.5

Solving
-4.5 + x = -3.5

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -3.5 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -3.5 + 4.5
x = -3.5 + 4.5

Combine like terms: -3.5 + 4.5 = 1
x = 1

Simplifying
x = 1

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8, 1}