234x^2-(2455x+568)=5668x-678

Solution for 234x^2-(2455x+568)=5668x-678 equation:

Simplifying
234x2 + -1(2455x + 568) = 5668x + -678

Reorder the terms:
234x2 + -1(568 + 2455x) = 5668x + -678
234x2 + (568 * -1 + 2455x * -1) = 5668x + -678
234x2 + (-568 + -2455x) = 5668x + -678

Reorder the terms:
-568 + -2455x + 234x2 = 5668x + -678

Reorder the terms:
-568 + -2455x + 234x2 = -678 + 5668x

Solving
-568 + -2455x + 234x2 = -678 + 5668x

Solving for variable 'x'.

Reorder the terms:
-568 + 678 + -2455x + -5668x + 234x2 = -678 + 5668x + 678 + -5668x

Combine like terms: -568 + 678 = 110
110 + -2455x + -5668x + 234x2 = -678 + 5668x + 678 + -5668x

Combine like terms: -2455x + -5668x = -8123x
110 + -8123x + 234x2 = -678 + 5668x + 678 + -5668x

Reorder the terms:
110 + -8123x + 234x2 = -678 + 678 + 5668x + -5668x

Combine like terms: -678 + 678 = 0
110 + -8123x + 234x2 = 0 + 5668x + -5668x
110 + -8123x + 234x2 = 5668x + -5668x

Combine like terms: 5668x + -5668x = 0
110 + -8123x + 234x2 = 0

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

Divide each side by '234'.
0.4700854701 + -34.71367521x + x2 = 0

Move the constant term to the right:

Add '-0.4700854701' to each side of the equation.
0.4700854701 + -34.71367521x + -0.4700854701 + x2 = 0 + -0.4700854701

Reorder the terms:
0.4700854701 + -0.4700854701 + -34.71367521x + x2 = 0 + -0.4700854701

Combine like terms: 0.4700854701 + -0.4700854701 = 0.0000000000
0.0000000000 + -34.71367521x + x2 = 0 + -0.4700854701
-34.71367521x + x2 = 0 + -0.4700854701

Combine like terms: 0 + -0.4700854701 = -0.4700854701
-34.71367521x + x2 = -0.4700854701

The x term is -34.71367521x.  Take half its coefficient (-17.35683761).
Square it (301.2598118) and add it to both sides.

Add '301.2598118' to each side of the equation.
-34.71367521x + 301.2598118 + x2 = -0.4700854701 + 301.2598118

Reorder the terms:
301.2598118 + -34.71367521x + x2 = -0.4700854701 + 301.2598118

Combine like terms: -0.4700854701 + 301.2598118 = 300.7897263299
301.2598118 + -34.71367521x + x2 = 300.7897263299

Factor a perfect square on the left side:
(x + -17.35683761)(x + -17.35683761) = 300.7897263299

Calculate the square root of the right side: 17.343290528

Break this problem into two subproblems by setting 
(x + -17.35683761) equal to 17.343290528 and -17.343290528.

Subproblem 1
x + -17.35683761 = 17.343290528

Simplifying
x + -17.35683761 = 17.343290528

Reorder the terms:
-17.35683761 + x = 17.343290528

Solving
-17.35683761 + x = 17.343290528

Solving for variable 'x'.

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

Add '17.35683761' to each side of the equation.
-17.35683761 + 17.35683761 + x = 17.343290528 + 17.35683761

Combine like terms: -17.35683761 + 17.35683761 = 0.00000000
0.00000000 + x = 17.343290528 + 17.35683761
x = 17.343290528 + 17.35683761

Combine like terms: 17.343290528 + 17.35683761 = 34.700128138
x = 34.700128138

Simplifying
x = 34.700128138

Subproblem 2
x + -17.35683761 = -17.343290528

Simplifying
x + -17.35683761 = -17.343290528

Reorder the terms:
-17.35683761 + x = -17.343290528

Solving
-17.35683761 + x = -17.343290528

Solving for variable 'x'.

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

Add '17.35683761' to each side of the equation.
-17.35683761 + 17.35683761 + x = -17.343290528 + 17.35683761

Combine like terms: -17.35683761 + 17.35683761 = 0.00000000
0.00000000 + x = -17.343290528 + 17.35683761
x = -17.343290528 + 17.35683761

Combine like terms: -17.343290528 + 17.35683761 = 0.013547082
x = 0.013547082

Simplifying
x = 0.013547082

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {34.700128138, 0.013547082}