-3x^2-5x+1=8x^2-2x-9

Solution for -3x^2-5x+1=8x^2-2x-9 equation:

Simplifying
-3x2 + -5x + 1 = 8x2 + -2x + -9

Reorder the terms:
1 + -5x + -3x2 = 8x2 + -2x + -9

Reorder the terms:
1 + -5x + -3x2 = -9 + -2x + 8x2

Solving
1 + -5x + -3x2 = -9 + -2x + 8x2

Solving for variable 'x'.

Reorder the terms:
1 + 9 + -5x + 2x + -3x2 + -8x2 = -9 + -2x + 8x2 + 9 + 2x + -8x2

Combine like terms: 1 + 9 = 10
10 + -5x + 2x + -3x2 + -8x2 = -9 + -2x + 8x2 + 9 + 2x + -8x2

Combine like terms: -5x + 2x = -3x
10 + -3x + -3x2 + -8x2 = -9 + -2x + 8x2 + 9 + 2x + -8x2

Combine like terms: -3x2 + -8x2 = -11x2
10 + -3x + -11x2 = -9 + -2x + 8x2 + 9 + 2x + -8x2

Reorder the terms:
10 + -3x + -11x2 = -9 + 9 + -2x + 2x + 8x2 + -8x2

Combine like terms: -9 + 9 = 0
10 + -3x + -11x2 = 0 + -2x + 2x + 8x2 + -8x2
10 + -3x + -11x2 = -2x + 2x + 8x2 + -8x2

Combine like terms: -2x + 2x = 0
10 + -3x + -11x2 = 0 + 8x2 + -8x2
10 + -3x + -11x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
10 + -3x + -11x2 = 0

Begin completing the square.  Divide all terms by
-11 the coefficient of the squared term: 

Divide each side by '-11'.
-0.9090909091 + 0.2727272727x + x2 = 0

Move the constant term to the right:

Add '0.9090909091' to each side of the equation.
-0.9090909091 + 0.2727272727x + 0.9090909091 + x2 = 0 + 0.9090909091

Reorder the terms:
-0.9090909091 + 0.9090909091 + 0.2727272727x + x2 = 0 + 0.9090909091

Combine like terms: -0.9090909091 + 0.9090909091 = 0.0000000000
0.0000000000 + 0.2727272727x + x2 = 0 + 0.9090909091
0.2727272727x + x2 = 0 + 0.9090909091

Combine like terms: 0 + 0.9090909091 = 0.9090909091
0.2727272727x + x2 = 0.9090909091

The x term is 0.2727272727x.  Take half its coefficient (0.1363636364).
Square it (0.01859504133) and add it to both sides.

Add '0.01859504133' to each side of the equation.
0.2727272727x + 0.01859504133 + x2 = 0.9090909091 + 0.01859504133

Reorder the terms:
0.01859504133 + 0.2727272727x + x2 = 0.9090909091 + 0.01859504133

Combine like terms: 0.9090909091 + 0.01859504133 = 0.92768595043
0.01859504133 + 0.2727272727x + x2 = 0.92768595043

Factor a perfect square on the left side:
(x + 0.1363636364)(x + 0.1363636364) = 0.92768595043

Calculate the square root of the right side: 0.96316455

Break this problem into two subproblems by setting 
(x + 0.1363636364) equal to 0.96316455 and -0.96316455.

Subproblem 1
x + 0.1363636364 = 0.96316455

Simplifying
x + 0.1363636364 = 0.96316455

Reorder the terms:
0.1363636364 + x = 0.96316455

Solving
0.1363636364 + x = 0.96316455

Solving for variable 'x'.

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

Add '-0.1363636364' to each side of the equation.
0.1363636364 + -0.1363636364 + x = 0.96316455 + -0.1363636364

Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000
0.0000000000 + x = 0.96316455 + -0.1363636364
x = 0.96316455 + -0.1363636364

Combine like terms: 0.96316455 + -0.1363636364 = 0.8268009136
x = 0.8268009136

Simplifying
x = 0.8268009136

Subproblem 2
x + 0.1363636364 = -0.96316455

Simplifying
x + 0.1363636364 = -0.96316455

Reorder the terms:
0.1363636364 + x = -0.96316455

Solving
0.1363636364 + x = -0.96316455

Solving for variable 'x'.

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

Add '-0.1363636364' to each side of the equation.
0.1363636364 + -0.1363636364 + x = -0.96316455 + -0.1363636364

Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000
0.0000000000 + x = -0.96316455 + -0.1363636364
x = -0.96316455 + -0.1363636364

Combine like terms: -0.96316455 + -0.1363636364 = -1.0995281864
x = -1.0995281864

Simplifying
x = -1.0995281864

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8268009136, -1.0995281864}