14.3+6x=3.9+2x(x+5.2)

Solution for 14.3+6x=3.9+2x(x+5.2) equation:

Simplifying
14.3 + 6x = 3.9 + 2x(x + 5.2)

Reorder the terms:
14.3 + 6x = 3.9 + 2x(5.2 + x)
14.3 + 6x = 3.9 + (5.2 * 2x + x * 2x)
14.3 + 6x = 3.9 + (10.4x + 2x2)

Solving
14.3 + 6x = 3.9 + 10.4x + 2x2

Solving for variable 'x'.

Reorder the terms:
14.3 + -3.9 + 6x + -10.4x + -2x2 = 3.9 + 10.4x + 2x2 + -3.9 + -10.4x + -2x2

Combine like terms: 14.3 + -3.9 = 10.4
10.4 + 6x + -10.4x + -2x2 = 3.9 + 10.4x + 2x2 + -3.9 + -10.4x + -2x2

Combine like terms: 6x + -10.4x = -4.4x
10.4 + -4.4x + -2x2 = 3.9 + 10.4x + 2x2 + -3.9 + -10.4x + -2x2

Reorder the terms:
10.4 + -4.4x + -2x2 = 3.9 + -3.9 + 10.4x + -10.4x + 2x2 + -2x2

Combine like terms: 3.9 + -3.9 = 0.0
10.4 + -4.4x + -2x2 = 0.0 + 10.4x + -10.4x + 2x2 + -2x2
10.4 + -4.4x + -2x2 = 10.4x + -10.4x + 2x2 + -2x2

Combine like terms: 10.4x + -10.4x = 0.0
10.4 + -4.4x + -2x2 = 0.0 + 2x2 + -2x2
10.4 + -4.4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
10.4 + -4.4x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-5.2 + 2.2x + x2 = 0

Move the constant term to the right:

Add '5.2' to each side of the equation.
-5.2 + 2.2x + 5.2 + x2 = 0 + 5.2

Reorder the terms:
-5.2 + 5.2 + 2.2x + x2 = 0 + 5.2

Combine like terms: -5.2 + 5.2 = 0.0
0.0 + 2.2x + x2 = 0 + 5.2
2.2x + x2 = 0 + 5.2

Combine like terms: 0 + 5.2 = 5.2
2.2x + x2 = 5.2

The x term is 2.2x.  Take half its coefficient (1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
2.2x + 1.21 + x2 = 5.2 + 1.21

Reorder the terms:
1.21 + 2.2x + x2 = 5.2 + 1.21

Combine like terms: 5.2 + 1.21 = 6.41
1.21 + 2.2x + x2 = 6.41

Factor a perfect square on the left side:
(x + 1.1)(x + 1.1) = 6.41

Calculate the square root of the right side: 2.53179778

Break this problem into two subproblems by setting 
(x + 1.1) equal to 2.53179778 and -2.53179778.

Subproblem 1
x + 1.1 = 2.53179778

Simplifying
x + 1.1 = 2.53179778

Reorder the terms:
1.1 + x = 2.53179778

Solving
1.1 + x = 2.53179778

Solving for variable 'x'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + x = 2.53179778 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + x = 2.53179778 + -1.1
x = 2.53179778 + -1.1

Combine like terms: 2.53179778 + -1.1 = 1.43179778
x = 1.43179778

Simplifying
x = 1.43179778

Subproblem 2
x + 1.1 = -2.53179778

Simplifying
x + 1.1 = -2.53179778

Reorder the terms:
1.1 + x = -2.53179778

Solving
1.1 + x = -2.53179778

Solving for variable 'x'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + x = -2.53179778 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + x = -2.53179778 + -1.1
x = -2.53179778 + -1.1

Combine like terms: -2.53179778 + -1.1 = -3.63179778
x = -3.63179778

Simplifying
x = -3.63179778

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.43179778, -3.63179778}