2x^2+5.2+3x+1.2+6.2=180

Solution for 2x^2+5.2+3x+1.2+6.2=180 equation:

Simplifying
2x2 + 5.2 + 3x + 1.2 + 6.2 = 180

Reorder the terms:
5.2 + 1.2 + 6.2 + 3x + 2x2 = 180

Combine like terms: 5.2 + 1.2 = 6.4
6.4 + 6.2 + 3x + 2x2 = 180

Combine like terms: 6.4 + 6.2 = 12.6
12.6 + 3x + 2x2 = 180

Solving
12.6 + 3x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
12.6 + -180 + 3x + 2x2 = 180 + -180

Combine like terms: 12.6 + -180 = -167.4
-167.4 + 3x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-167.4 + 3x + 2x2 = 0

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

Divide each side by '2'.
-83.7 + 1.5x + x2 = 0

Move the constant term to the right:

Add '83.7' to each side of the equation.
-83.7 + 1.5x + 83.7 + x2 = 0 + 83.7

Reorder the terms:
-83.7 + 83.7 + 1.5x + x2 = 0 + 83.7

Combine like terms: -83.7 + 83.7 = 0.0
0.0 + 1.5x + x2 = 0 + 83.7
1.5x + x2 = 0 + 83.7

Combine like terms: 0 + 83.7 = 83.7
1.5x + x2 = 83.7

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 83.7 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 83.7 + 0.5625

Combine like terms: 83.7 + 0.5625 = 84.2625
0.5625 + 1.5x + x2 = 84.2625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 84.2625

Calculate the square root of the right side: 9.179460768

Break this problem into two subproblems by setting 
(x + 0.75) equal to 9.179460768 and -9.179460768.

Subproblem 1
x + 0.75 = 9.179460768

Simplifying
x + 0.75 = 9.179460768

Reorder the terms:
0.75 + x = 9.179460768

Solving
0.75 + x = 9.179460768

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 9.179460768 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 9.179460768 + -0.75
x = 9.179460768 + -0.75

Combine like terms: 9.179460768 + -0.75 = 8.429460768
x = 8.429460768

Simplifying
x = 8.429460768

Subproblem 2
x + 0.75 = -9.179460768

Simplifying
x + 0.75 = -9.179460768

Reorder the terms:
0.75 + x = -9.179460768

Solving
0.75 + x = -9.179460768

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -9.179460768 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -9.179460768 + -0.75
x = -9.179460768 + -0.75

Combine like terms: -9.179460768 + -0.75 = -9.929460768
x = -9.929460768

Simplifying
x = -9.929460768

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.429460768, -9.929460768}