20x^2-27x+8=0

Solution for 20x^2-27x+8=0 equation:

Simplifying
20x2 + -27x + 8 = 0

Reorder the terms:
8 + -27x + 20x2 = 0

Solving
8 + -27x + 20x2 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
0.4 + -1.35x + x2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -1.35x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -1.35x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -1.35x + x2 = 0 + -0.4
-1.35x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-1.35x + x2 = -0.4

The x term is -1.35x.  Take half its coefficient (-0.675).
Square it (0.455625) and add it to both sides.

Add '0.455625' to each side of the equation.
-1.35x + 0.455625 + x2 = -0.4 + 0.455625

Reorder the terms:
0.455625 + -1.35x + x2 = -0.4 + 0.455625

Combine like terms: -0.4 + 0.455625 = 0.055625
0.455625 + -1.35x + x2 = 0.055625

Factor a perfect square on the left side:
(x + -0.675)(x + -0.675) = 0.055625

Calculate the square root of the right side: 0.235849528

Break this problem into two subproblems by setting 
(x + -0.675) equal to 0.235849528 and -0.235849528.

Subproblem 1
x + -0.675 = 0.235849528

Simplifying
x + -0.675 = 0.235849528

Reorder the terms:
-0.675 + x = 0.235849528

Solving
-0.675 + x = 0.235849528

Solving for variable 'x'.

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

Add '0.675' to each side of the equation.
-0.675 + 0.675 + x = 0.235849528 + 0.675

Combine like terms: -0.675 + 0.675 = 0.000
0.000 + x = 0.235849528 + 0.675
x = 0.235849528 + 0.675

Combine like terms: 0.235849528 + 0.675 = 0.910849528
x = 0.910849528

Simplifying
x = 0.910849528

Subproblem 2
x + -0.675 = -0.235849528

Simplifying
x + -0.675 = -0.235849528

Reorder the terms:
-0.675 + x = -0.235849528

Solving
-0.675 + x = -0.235849528

Solving for variable 'x'.

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

Add '0.675' to each side of the equation.
-0.675 + 0.675 + x = -0.235849528 + 0.675

Combine like terms: -0.675 + 0.675 = 0.000
0.000 + x = -0.235849528 + 0.675
x = -0.235849528 + 0.675

Combine like terms: -0.235849528 + 0.675 = 0.439150472
x = 0.439150472

Simplifying
x = 0.439150472

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.910849528, 0.439150472}