-0.9x^2-2.7x+16.2=0

Solution for -0.9x^2-2.7x+16.2=0 equation:

Simplifying
-0.9x2 + -2.7x + 16.2 = 0

Reorder the terms:
16.2 + -2.7x + -0.9x2 = 0

Solving
16.2 + -2.7x + -0.9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.9 the coefficient of the squared term: 

Divide each side by '-0.9'.
-18 + 3x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 3x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 3x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 3x + x2 = 0 + 18
3x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
3x + x2 = 18

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 = 18 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 18 + 2.25

Combine like terms: 18 + 2.25 = 20.25
2.25 + 3x + x2 = 20.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 20.25

Calculate the square root of the right side: 4.5

Break this problem into two subproblems by setting 
(x + 1.5) equal to 4.5 and -4.5.

Subproblem 1
x + 1.5 = 4.5

Simplifying
x + 1.5 = 4.5

Reorder the terms:
1.5 + x = 4.5

Solving
1.5 + x = 4.5

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 = 4.5 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 4.5 + -1.5
x = 4.5 + -1.5

Combine like terms: 4.5 + -1.5 = 3
x = 3

Simplifying
x = 3

Subproblem 2
x + 1.5 = -4.5

Simplifying
x + 1.5 = -4.5

Reorder the terms:
1.5 + x = -4.5

Solving
1.5 + x = -4.5

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 = -4.5 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -4.5 + -1.5
x = -4.5 + -1.5

Combine like terms: -4.5 + -1.5 = -6
x = -6

Simplifying
x = -6

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3, -6}