3x^2+140x+1200=0

Solution for 3x^2+140x+1200=0 equation:

Simplifying
3x2 + 140x + 1200 = 0

Reorder the terms:
1200 + 140x + 3x2 = 0

Solving
1200 + 140x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
400 + 46.66666667x + x2 = 0

Move the constant term to the right:

Add '-400' to each side of the equation.
400 + 46.66666667x + -400 + x2 = 0 + -400

Reorder the terms:
400 + -400 + 46.66666667x + x2 = 0 + -400

Combine like terms: 400 + -400 = 0
0 + 46.66666667x + x2 = 0 + -400
46.66666667x + x2 = 0 + -400

Combine like terms: 0 + -400 = -400
46.66666667x + x2 = -400

The x term is 46.66666667x.  Take half its coefficient (23.33333334).
Square it (544.4444448) and add it to both sides.

Add '544.4444448' to each side of the equation.
46.66666667x + 544.4444448 + x2 = -400 + 544.4444448

Reorder the terms:
544.4444448 + 46.66666667x + x2 = -400 + 544.4444448

Combine like terms: -400 + 544.4444448 = 144.4444448
544.4444448 + 46.66666667x + x2 = 144.4444448

Factor a perfect square on the left side:
(x + 23.33333334)(x + 23.33333334) = 144.4444448

Calculate the square root of the right side: 12.018504266

Break this problem into two subproblems by setting 
(x + 23.33333334) equal to 12.018504266 and -12.018504266.

Subproblem 1
x + 23.33333334 = 12.018504266

Simplifying
x + 23.33333334 = 12.018504266

Reorder the terms:
23.33333334 + x = 12.018504266

Solving
23.33333334 + x = 12.018504266

Solving for variable 'x'.

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

Add '-23.33333334' to each side of the equation.
23.33333334 + -23.33333334 + x = 12.018504266 + -23.33333334

Combine like terms: 23.33333334 + -23.33333334 = 0.00000000
0.00000000 + x = 12.018504266 + -23.33333334
x = 12.018504266 + -23.33333334

Combine like terms: 12.018504266 + -23.33333334 = -11.314829074
x = -11.314829074

Simplifying
x = -11.314829074

Subproblem 2
x + 23.33333334 = -12.018504266

Simplifying
x + 23.33333334 = -12.018504266

Reorder the terms:
23.33333334 + x = -12.018504266

Solving
23.33333334 + x = -12.018504266

Solving for variable 'x'.

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

Add '-23.33333334' to each side of the equation.
23.33333334 + -23.33333334 + x = -12.018504266 + -23.33333334

Combine like terms: 23.33333334 + -23.33333334 = 0.00000000
0.00000000 + x = -12.018504266 + -23.33333334
x = -12.018504266 + -23.33333334

Combine like terms: -12.018504266 + -23.33333334 = -35.351837606
x = -35.351837606

Simplifying
x = -35.351837606

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-11.314829074, -35.351837606}