143.3x^2+1823.3x+6820x=4

Solution for 143.3x^2+1823.3x+6820x=4 equation:

Simplifying
143.3x2 + 1823.3x + 6820x = 4

Reorder the terms:
1823.3x + 6820x + 143.3x2 = 4

Combine like terms: 1823.3x + 6820x = 8643.3x
8643.3x + 143.3x2 = 4

Solving
8643.3x + 143.3x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 8643.3x + 143.3x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 8643.3x + 143.3x2 = 0

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

Divide each side by '143.3'.
-0.02791346825 + 60.31612003x + x2 = 0

Move the constant term to the right:

Add '0.02791346825' to each side of the equation.
-0.02791346825 + 60.31612003x + 0.02791346825 + x2 = 0 + 0.02791346825

Reorder the terms:
-0.02791346825 + 0.02791346825 + 60.31612003x + x2 = 0 + 0.02791346825

Combine like terms: -0.02791346825 + 0.02791346825 = 0.00000000000
0.00000000000 + 60.31612003x + x2 = 0 + 0.02791346825
60.31612003x + x2 = 0 + 0.02791346825

Combine like terms: 0 + 0.02791346825 = 0.02791346825
60.31612003x + x2 = 0.02791346825

The x term is 60.31612003x.  Take half its coefficient (30.15806002).
Square it (909.5085842) and add it to both sides.

Add '909.5085842' to each side of the equation.
60.31612003x + 909.5085842 + x2 = 0.02791346825 + 909.5085842

Reorder the terms:
909.5085842 + 60.31612003x + x2 = 0.02791346825 + 909.5085842

Combine like terms: 0.02791346825 + 909.5085842 = 909.53649766825
909.5085842 + 60.31612003x + x2 = 909.53649766825

Factor a perfect square on the left side:
(x + 30.15806002)(x + 30.15806002) = 909.53649766825

Calculate the square root of the right side: 30.158522803

Break this problem into two subproblems by setting 
(x + 30.15806002) equal to 30.158522803 and -30.158522803.

Subproblem 1
x + 30.15806002 = 30.158522803

Simplifying
x + 30.15806002 = 30.158522803

Reorder the terms:
30.15806002 + x = 30.158522803

Solving
30.15806002 + x = 30.158522803

Solving for variable 'x'.

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

Add '-30.15806002' to each side of the equation.
30.15806002 + -30.15806002 + x = 30.158522803 + -30.15806002

Combine like terms: 30.15806002 + -30.15806002 = 0.00000000
0.00000000 + x = 30.158522803 + -30.15806002
x = 30.158522803 + -30.15806002

Combine like terms: 30.158522803 + -30.15806002 = 0.000462783
x = 0.000462783

Simplifying
x = 0.000462783

Subproblem 2
x + 30.15806002 = -30.158522803

Simplifying
x + 30.15806002 = -30.158522803

Reorder the terms:
30.15806002 + x = -30.158522803

Solving
30.15806002 + x = -30.158522803

Solving for variable 'x'.

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

Add '-30.15806002' to each side of the equation.
30.15806002 + -30.15806002 + x = -30.158522803 + -30.15806002

Combine like terms: 30.15806002 + -30.15806002 = 0.00000000
0.00000000 + x = -30.158522803 + -30.15806002
x = -30.158522803 + -30.15806002

Combine like terms: -30.158522803 + -30.15806002 = -60.316582823
x = -60.316582823

Simplifying
x = -60.316582823

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.000462783, -60.316582823}