6=-20x^2+320x-780

Solution for 6=-20x^2+320x-780 equation:

Simplifying
6 = -20x2 + 320x + -780

Reorder the terms:
6 = -780 + 320x + -20x2

Solving
6 = -780 + 320x + -20x2

Solving for variable 'x'.

Combine like terms: 6 + 780 = 786
786 + -320x + 20x2 = -780 + 320x + -20x2 + 780 + -320x + 20x2

Reorder the terms:
786 + -320x + 20x2 = -780 + 780 + 320x + -320x + -20x2 + 20x2

Combine like terms: -780 + 780 = 0
786 + -320x + 20x2 = 0 + 320x + -320x + -20x2 + 20x2
786 + -320x + 20x2 = 320x + -320x + -20x2 + 20x2

Combine like terms: 320x + -320x = 0
786 + -320x + 20x2 = 0 + -20x2 + 20x2
786 + -320x + 20x2 = -20x2 + 20x2

Combine like terms: -20x2 + 20x2 = 0
786 + -320x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(393 + -160x + 10x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(393 + -160x + 10x2)' equal to zero and attempt to solve:

Simplifying
393 + -160x + 10x2 = 0

Solving
393 + -160x + 10x2 = 0

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

Divide each side by '10'.
39.3 + -16x + x2 = 0.0

Move the constant term to the right:

Add '-39.3' to each side of the equation.
39.3 + -16x + -39.3 + x2 = 0.0 + -39.3

Reorder the terms:
39.3 + -39.3 + -16x + x2 = 0.0 + -39.3

Combine like terms: 39.3 + -39.3 = 0.0
0.0 + -16x + x2 = 0.0 + -39.3
-16x + x2 = 0.0 + -39.3

Combine like terms: 0.0 + -39.3 = -39.3
-16x + x2 = -39.3

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -39.3 + 64

Reorder the terms:
64 + -16x + x2 = -39.3 + 64

Combine like terms: -39.3 + 64 = 24.7
64 + -16x + x2 = 24.7

Factor a perfect square on the left side:
(x + -8)(x + -8) = 24.7

Calculate the square root of the right side: 4.969909456

Break this problem into two subproblems by setting 
(x + -8) equal to 4.969909456 and -4.969909456.

Subproblem 1
x + -8 = 4.969909456

Simplifying
x + -8 = 4.969909456

Reorder the terms:
-8 + x = 4.969909456

Solving
-8 + x = 4.969909456

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 4.969909456 + 8

Combine like terms: -8 + 8 = 0
0 + x = 4.969909456 + 8
x = 4.969909456 + 8

Combine like terms: 4.969909456 + 8 = 12.969909456
x = 12.969909456

Simplifying
x = 12.969909456

Subproblem 2
x + -8 = -4.969909456

Simplifying
x + -8 = -4.969909456

Reorder the terms:
-8 + x = -4.969909456

Solving
-8 + x = -4.969909456

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -4.969909456 + 8

Combine like terms: -8 + 8 = 0
0 + x = -4.969909456 + 8
x = -4.969909456 + 8

Combine like terms: -4.969909456 + 8 = 3.030090544
x = 3.030090544

Simplifying
x = 3.030090544

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.969909456, 3.030090544}
Solution
x = {12.969909456, 3.030090544}