264306=115000x^2+9114x

Solution for 264306=115000x^2+9114x equation:

Simplifying
264306 = 115000x2 + 9114x

Reorder the terms:
264306 = 9114x + 115000x2

Solving
264306 = 9114x + 115000x2

Solving for variable 'x'.

Reorder the terms:
264306 + -9114x + -115000x2 = 9114x + -9114x + 115000x2 + -115000x2

Combine like terms: 9114x + -9114x = 0
264306 + -9114x + -115000x2 = 0 + 115000x2 + -115000x2
264306 + -9114x + -115000x2 = 115000x2 + -115000x2

Combine like terms: 115000x2 + -115000x2 = 0
264306 + -9114x + -115000x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(132153 + -4557x + -57500x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(132153 + -4557x + -57500x2)' equal to zero and attempt to solve:

Simplifying
132153 + -4557x + -57500x2 = 0

Solving
132153 + -4557x + -57500x2 = 0

Begin completing the square.  Divide all terms by
-57500 the coefficient of the squared term: 

Divide each side by '-57500'.
-2.298313043 + 0.07925217391x + x2 = 0.00

Move the constant term to the right:

Add '2.298313043' to each side of the equation.
-2.298313043 + 0.07925217391x + 2.298313043 + x2 = 0.00 + 2.298313043

Reorder the terms:
-2.298313043 + 2.298313043 + 0.07925217391x + x2 = 0.00 + 2.298313043

Combine like terms: -2.298313043 + 2.298313043 = 0.000000000
0.000000000 + 0.07925217391x + x2 = 0.00 + 2.298313043
0.07925217391x + x2 = 0.00 + 2.298313043

Combine like terms: 0.00 + 2.298313043 = 2.298313043
0.07925217391x + x2 = 2.298313043

The x term is 0.07925217391x.  Take half its coefficient (0.03962608696).
Square it (0.001570226768) and add it to both sides.

Add '0.001570226768' to each side of the equation.
0.07925217391x + 0.001570226768 + x2 = 2.298313043 + 0.001570226768

Reorder the terms:
0.001570226768 + 0.07925217391x + x2 = 2.298313043 + 0.001570226768

Combine like terms: 2.298313043 + 0.001570226768 = 2.299883269768
0.001570226768 + 0.07925217391x + x2 = 2.299883269768

Factor a perfect square on the left side:
(x + 0.03962608696)(x + 0.03962608696) = 2.299883269768

Calculate the square root of the right side: 1.516536604

Break this problem into two subproblems by setting 
(x + 0.03962608696) equal to 1.516536604 and -1.516536604.

Subproblem 1
x + 0.03962608696 = 1.516536604

Simplifying
x + 0.03962608696 = 1.516536604

Reorder the terms:
0.03962608696 + x = 1.516536604

Solving
0.03962608696 + x = 1.516536604

Solving for variable 'x'.

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

Add '-0.03962608696' to each side of the equation.
0.03962608696 + -0.03962608696 + x = 1.516536604 + -0.03962608696

Combine like terms: 0.03962608696 + -0.03962608696 = 0.00000000000
0.00000000000 + x = 1.516536604 + -0.03962608696
x = 1.516536604 + -0.03962608696

Combine like terms: 1.516536604 + -0.03962608696 = 1.47691051704
x = 1.47691051704

Simplifying
x = 1.47691051704

Subproblem 2
x + 0.03962608696 = -1.516536604

Simplifying
x + 0.03962608696 = -1.516536604

Reorder the terms:
0.03962608696 + x = -1.516536604

Solving
0.03962608696 + x = -1.516536604

Solving for variable 'x'.

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

Add '-0.03962608696' to each side of the equation.
0.03962608696 + -0.03962608696 + x = -1.516536604 + -0.03962608696

Combine like terms: 0.03962608696 + -0.03962608696 = 0.00000000000
0.00000000000 + x = -1.516536604 + -0.03962608696
x = -1.516536604 + -0.03962608696

Combine like terms: -1.516536604 + -0.03962608696 = -1.55616269096
x = -1.55616269096

Simplifying
x = -1.55616269096

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.47691051704, -1.55616269096}
Solution
x = {1.47691051704, -1.55616269096}