9x^2+3-80x+6=x-3

Solution for 9x^2+3-80x+6=x-3 equation:

Simplifying
9x2 + 3 + -80x + 6 = x + -3

Reorder the terms:
3 + 6 + -80x + 9x2 = x + -3

Combine like terms: 3 + 6 = 9
9 + -80x + 9x2 = x + -3

Reorder the terms:
9 + -80x + 9x2 = -3 + x

Solving
9 + -80x + 9x2 = -3 + x

Solving for variable 'x'.

Reorder the terms:
9 + 3 + -80x + -1x + 9x2 = -3 + x + 3 + -1x

Combine like terms: 9 + 3 = 12
12 + -80x + -1x + 9x2 = -3 + x + 3 + -1x

Combine like terms: -80x + -1x = -81x
12 + -81x + 9x2 = -3 + x + 3 + -1x

Reorder the terms:
12 + -81x + 9x2 = -3 + 3 + x + -1x

Combine like terms: -3 + 3 = 0
12 + -81x + 9x2 = 0 + x + -1x
12 + -81x + 9x2 = x + -1x

Combine like terms: x + -1x = 0
12 + -81x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -27x + 3x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + -27x + 3x2)' equal to zero and attempt to solve:

Simplifying
4 + -27x + 3x2 = 0

Solving
4 + -27x + 3x2 = 0

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

Divide each side by '3'.
1.333333333 + -9x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -9x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -9x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -9x + x2 = 0 + -1.333333333
-9x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-9x + x2 = -1.333333333

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -1.333333333 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -1.333333333 + 20.25

Combine like terms: -1.333333333 + 20.25 = 18.916666667
20.25 + -9x + x2 = 18.916666667

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 18.916666667

Calculate the square root of the right side: 4.34932945

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.34932945 and -4.34932945.

Subproblem 1
x + -4.5 = 4.34932945

Simplifying
x + -4.5 = 4.34932945

Reorder the terms:
-4.5 + x = 4.34932945

Solving
-4.5 + x = 4.34932945

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 4.34932945 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 4.34932945 + 4.5
x = 4.34932945 + 4.5

Combine like terms: 4.34932945 + 4.5 = 8.84932945
x = 8.84932945

Simplifying
x = 8.84932945

Subproblem 2
x + -4.5 = -4.34932945

Simplifying
x + -4.5 = -4.34932945

Reorder the terms:
-4.5 + x = -4.34932945

Solving
-4.5 + x = -4.34932945

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -4.34932945 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -4.34932945 + 4.5
x = -4.34932945 + 4.5

Combine like terms: -4.34932945 + 4.5 = 0.15067055
x = 0.15067055

Simplifying
x = 0.15067055

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.84932945, 0.15067055}
Solution
x = {8.84932945, 0.15067055}