x=(5x^2-3x+9)-(20x^2+11x-6)

Solution for x=(5x^2-3x+9)-(20x^2+11x-6) equation:

Simplifying
x = (5x2 + -3x + 9) + -1(20x2 + 11x + -6)

Reorder the terms:
x = (9 + -3x + 5x2) + -1(20x2 + 11x + -6)

Remove parenthesis around (9 + -3x + 5x2)
x = 9 + -3x + 5x2 + -1(20x2 + 11x + -6)

Reorder the terms:
x = 9 + -3x + 5x2 + -1(-6 + 11x + 20x2)
x = 9 + -3x + 5x2 + (-6 * -1 + 11x * -1 + 20x2 * -1)
x = 9 + -3x + 5x2 + (6 + -11x + -20x2)

Reorder the terms:
x = 9 + 6 + -3x + -11x + 5x2 + -20x2

Combine like terms: 9 + 6 = 15
x = 15 + -3x + -11x + 5x2 + -20x2

Combine like terms: -3x + -11x = -14x
x = 15 + -14x + 5x2 + -20x2

Combine like terms: 5x2 + -20x2 = -15x2
x = 15 + -14x + -15x2

Solving
x = 15 + -14x + -15x2

Solving for variable 'x'.

Reorder the terms:
-15 + x + 14x + 15x2 = 15 + -14x + -15x2 + -15 + 14x + 15x2

Combine like terms: x + 14x = 15x
-15 + 15x + 15x2 = 15 + -14x + -15x2 + -15 + 14x + 15x2

Reorder the terms:
-15 + 15x + 15x2 = 15 + -15 + -14x + 14x + -15x2 + 15x2

Combine like terms: 15 + -15 = 0
-15 + 15x + 15x2 = 0 + -14x + 14x + -15x2 + 15x2
-15 + 15x + 15x2 = -14x + 14x + -15x2 + 15x2

Combine like terms: -14x + 14x = 0
-15 + 15x + 15x2 = 0 + -15x2 + 15x2
-15 + 15x + 15x2 = -15x2 + 15x2

Combine like terms: -15x2 + 15x2 = 0
-15 + 15x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-1 + x + x2) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(-1 + x + x2)' equal to zero and attempt to solve:

Simplifying
-1 + x + x2 = 0

Solving
-1 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x + x2 = 0 + 1
x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
x + x2 = 1

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 1 + 0.25

Reorder the terms:
0.25 + x + x2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + x + x2 = 1.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
x + 0.5 = 1.118033989

Simplifying
x + 0.5 = 1.118033989

Reorder the terms:
0.5 + x = 1.118033989

Solving
0.5 + x = 1.118033989

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.118033989 + -0.5
x = 1.118033989 + -0.5

Combine like terms: 1.118033989 + -0.5 = 0.618033989
x = 0.618033989

Simplifying
x = 0.618033989

Subproblem 2
x + 0.5 = -1.118033989

Simplifying
x + 0.5 = -1.118033989

Reorder the terms:
0.5 + x = -1.118033989

Solving
0.5 + x = -1.118033989

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.118033989 + -0.5
x = -1.118033989 + -0.5

Combine like terms: -1.118033989 + -0.5 = -1.618033989
x = -1.618033989

Simplifying
x = -1.618033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.618033989, -1.618033989}
Solution
x = {0.618033989, -1.618033989}