-18x^2-39x+20=0

Solution for -18x^2-39x+20=0 equation:

Simplifying
-18x2 + -39x + 20 = 0

Reorder the terms:
20 + -39x + -18x2 = 0

Solving
20 + -39x + -18x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-18 the coefficient of the squared term: 

Divide each side by '-18'.
-1.111111111 + 2.166666667x + x2 = 0

Move the constant term to the right:

Add '1.111111111' to each side of the equation.
-1.111111111 + 2.166666667x + 1.111111111 + x2 = 0 + 1.111111111

Reorder the terms:
-1.111111111 + 1.111111111 + 2.166666667x + x2 = 0 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + 2.166666667x + x2 = 0 + 1.111111111
2.166666667x + x2 = 0 + 1.111111111

Combine like terms: 0 + 1.111111111 = 1.111111111
2.166666667x + x2 = 1.111111111

The x term is 2.166666667x.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667x + 1.173611113 + x2 = 1.111111111 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667x + x2 = 1.111111111 + 1.173611113

Combine like terms: 1.111111111 + 1.173611113 = 2.284722224
1.173611113 + 2.166666667x + x2 = 2.284722224

Factor a perfect square on the left side:
(x + 1.083333334)(x + 1.083333334) = 2.284722224

Calculate the square root of the right side: 1.511529763

Break this problem into two subproblems by setting 
(x + 1.083333334) equal to 1.511529763 and -1.511529763.

Subproblem 1
x + 1.083333334 = 1.511529763

Simplifying
x + 1.083333334 = 1.511529763

Reorder the terms:
1.083333334 + x = 1.511529763

Solving
1.083333334 + x = 1.511529763

Solving for variable 'x'.

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

Add '-1.083333334' to each side of the equation.
1.083333334 + -1.083333334 + x = 1.511529763 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + x = 1.511529763 + -1.083333334
x = 1.511529763 + -1.083333334

Combine like terms: 1.511529763 + -1.083333334 = 0.428196429
x = 0.428196429

Simplifying
x = 0.428196429

Subproblem 2
x + 1.083333334 = -1.511529763

Simplifying
x + 1.083333334 = -1.511529763

Reorder the terms:
1.083333334 + x = -1.511529763

Solving
1.083333334 + x = -1.511529763

Solving for variable 'x'.

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

Add '-1.083333334' to each side of the equation.
1.083333334 + -1.083333334 + x = -1.511529763 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + x = -1.511529763 + -1.083333334
x = -1.511529763 + -1.083333334

Combine like terms: -1.511529763 + -1.083333334 = -2.594863097
x = -2.594863097

Simplifying
x = -2.594863097

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.428196429, -2.594863097}