9x^2+15x+52=352000000

Solution for 9x^2+15x+52=352000000 equation:

Simplifying
9x2 + 15x + 52 = 352000000

Reorder the terms:
52 + 15x + 9x2 = 352000000

Solving
52 + 15x + 9x2 = 352000000

Solving for variable 'x'.

Reorder the terms:
52 + -352000000 + 15x + 9x2 = 352000000 + -352000000

Combine like terms: 52 + -352000000 = -351999948
-351999948 + 15x + 9x2 = 352000000 + -352000000

Combine like terms: 352000000 + -352000000 = 0
-351999948 + 15x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-117333316 + 5x + 3x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-117333316 + 5x + 3x2)' equal to zero and attempt to solve:

Simplifying
-117333316 + 5x + 3x2 = 0

Solving
-117333316 + 5x + 3x2 = 0

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

Divide each side by '3'.
-39111105.33 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '39111105.33' to each side of the equation.
-39111105.33 + 1.666666667x + 39111105.33 + x2 = 0 + 39111105.33

Reorder the terms:
-39111105.33 + 39111105.33 + 1.666666667x + x2 = 0 + 39111105.33

Combine like terms: -39111105.33 + 39111105.33 = 0.00
0.00 + 1.666666667x + x2 = 0 + 39111105.33
1.666666667x + x2 = 0 + 39111105.33

Combine like terms: 0 + 39111105.33 = 39111105.33
1.666666667x + x2 = 39111105.33

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 39111105.33 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 39111105.33 + 0.6944444447

Combine like terms: 39111105.33 + 0.6944444447 = 39111106.0244444447
0.6944444447 + 1.666666667x + x2 = 39111106.0244444447

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 39111106.0244444447

Calculate the square root of the right side: 6253.887273084

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 6253.887273084 and -6253.887273084.

Subproblem 1
x + 0.8333333335 = 6253.887273084

Simplifying
x + 0.8333333335 = 6253.887273084

Reorder the terms:
0.8333333335 + x = 6253.887273084

Solving
0.8333333335 + x = 6253.887273084

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 6253.887273084 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 6253.887273084 + -0.8333333335
x = 6253.887273084 + -0.8333333335

Combine like terms: 6253.887273084 + -0.8333333335 = 6253.0539397505
x = 6253.0539397505

Simplifying
x = 6253.0539397505

Subproblem 2
x + 0.8333333335 = -6253.887273084

Simplifying
x + 0.8333333335 = -6253.887273084

Reorder the terms:
0.8333333335 + x = -6253.887273084

Solving
0.8333333335 + x = -6253.887273084

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -6253.887273084 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -6253.887273084 + -0.8333333335
x = -6253.887273084 + -0.8333333335

Combine like terms: -6253.887273084 + -0.8333333335 = -6254.7206064175
x = -6254.7206064175

Simplifying
x = -6254.7206064175

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6253.0539397505, -6254.7206064175}
Solution
x = {6253.0539397505, -6254.7206064175}