12354=-143.3x^2+1823.3x+6820

Solution for 12354=-143.3x^2+1823.3x+6820 equation:

Simplifying
12354 = -143.3x2 + 1823.3x + 6820

Reorder the terms:
12354 = 6820 + 1823.3x + -143.3x2

Solving
12354 = 6820 + 1823.3x + -143.3x2

Solving for variable 'x'.

Combine like terms: 12354 + -6820 = 5534
5534 + -1823.3x + 143.3x2 = 6820 + 1823.3x + -143.3x2 + -6820 + -1823.3x + 143.3x2

Reorder the terms:
5534 + -1823.3x + 143.3x2 = 6820 + -6820 + 1823.3x + -1823.3x + -143.3x2 + 143.3x2

Combine like terms: 6820 + -6820 = 0
5534 + -1823.3x + 143.3x2 = 0 + 1823.3x + -1823.3x + -143.3x2 + 143.3x2
5534 + -1823.3x + 143.3x2 = 1823.3x + -1823.3x + -143.3x2 + 143.3x2

Combine like terms: 1823.3x + -1823.3x = 0.0
5534 + -1823.3x + 143.3x2 = 0.0 + -143.3x2 + 143.3x2
5534 + -1823.3x + 143.3x2 = -143.3x2 + 143.3x2

Combine like terms: -143.3x2 + 143.3x2 = 0.0
5534 + -1823.3x + 143.3x2 = 0.0

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

Divide each side by '143.3'.
38.61828332 + -12.72365666x + x2 = 0

Move the constant term to the right:

Add '-38.61828332' to each side of the equation.
38.61828332 + -12.72365666x + -38.61828332 + x2 = 0 + -38.61828332

Reorder the terms:
38.61828332 + -38.61828332 + -12.72365666x + x2 = 0 + -38.61828332

Combine like terms: 38.61828332 + -38.61828332 = 0.00000000
0.00000000 + -12.72365666x + x2 = 0 + -38.61828332
-12.72365666x + x2 = 0 + -38.61828332

Combine like terms: 0 + -38.61828332 = -38.61828332
-12.72365666x + x2 = -38.61828332

The x term is -12.72365666x.  Take half its coefficient (-6.36182833).
Square it (40.47285970) and add it to both sides.

Add '40.47285970' to each side of the equation.
-12.72365666x + 40.47285970 + x2 = -38.61828332 + 40.47285970

Reorder the terms:
40.47285970 + -12.72365666x + x2 = -38.61828332 + 40.47285970

Combine like terms: -38.61828332 + 40.47285970 = 1.85457638
40.47285970 + -12.72365666x + x2 = 1.85457638

Factor a perfect square on the left side:
(x + -6.36182833)(x + -6.36182833) = 1.85457638

Calculate the square root of the right side: 1.361828323

Break this problem into two subproblems by setting 
(x + -6.36182833) equal to 1.361828323 and -1.361828323.

Subproblem 1
x + -6.36182833 = 1.361828323

Simplifying
x + -6.36182833 = 1.361828323

Reorder the terms:
-6.36182833 + x = 1.361828323

Solving
-6.36182833 + x = 1.361828323

Solving for variable 'x'.

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

Add '6.36182833' to each side of the equation.
-6.36182833 + 6.36182833 + x = 1.361828323 + 6.36182833

Combine like terms: -6.36182833 + 6.36182833 = 0.00000000
0.00000000 + x = 1.361828323 + 6.36182833
x = 1.361828323 + 6.36182833

Combine like terms: 1.361828323 + 6.36182833 = 7.723656653
x = 7.723656653

Simplifying
x = 7.723656653

Subproblem 2
x + -6.36182833 = -1.361828323

Simplifying
x + -6.36182833 = -1.361828323

Reorder the terms:
-6.36182833 + x = -1.361828323

Solving
-6.36182833 + x = -1.361828323

Solving for variable 'x'.

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

Add '6.36182833' to each side of the equation.
-6.36182833 + 6.36182833 + x = -1.361828323 + 6.36182833

Combine like terms: -6.36182833 + 6.36182833 = 0.00000000
0.00000000 + x = -1.361828323 + 6.36182833
x = -1.361828323 + 6.36182833

Combine like terms: -1.361828323 + 6.36182833 = 5.000000007
x = 5.000000007

Simplifying
x = 5.000000007

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.723656653, 5.000000007}