6x^2+2x-1500=0

Solution for 6x^2+2x-1500=0 equation:

Simplifying
6x2 + 2x + -1500 = 0

Reorder the terms:
-1500 + 2x + 6x2 = 0

Solving
-1500 + 2x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-750 + x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-750 + x + 3x2)' equal to zero and attempt to solve:

Simplifying
-750 + x + 3x2 = 0

Solving
-750 + x + 3x2 = 0

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

Divide each side by '3'.
-250 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '250' to each side of the equation.
-250 + 0.3333333333x + 250 + x2 = 0 + 250

Reorder the terms:
-250 + 250 + 0.3333333333x + x2 = 0 + 250

Combine like terms: -250 + 250 = 0
0 + 0.3333333333x + x2 = 0 + 250
0.3333333333x + x2 = 0 + 250

Combine like terms: 0 + 250 = 250
0.3333333333x + x2 = 250

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333x + 0.25 + x2 = 250 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = 250 + 0.25

Combine like terms: 250 + 0.25 = 250.25
0.25 + 0.3333333333x + x2 = 250.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 250.25

Calculate the square root of the right side: 15.81929202

Break this problem into two subproblems by setting 
(x + 0.5) equal to 15.81929202 and -15.81929202.

Subproblem 1
x + 0.5 = 15.81929202

Simplifying
x + 0.5 = 15.81929202

Reorder the terms:
0.5 + x = 15.81929202

Solving
0.5 + x = 15.81929202

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 15.81929202 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 15.81929202 + -0.5
x = 15.81929202 + -0.5

Combine like terms: 15.81929202 + -0.5 = 15.31929202
x = 15.31929202

Simplifying
x = 15.31929202

Subproblem 2
x + 0.5 = -15.81929202

Simplifying
x + 0.5 = -15.81929202

Reorder the terms:
0.5 + x = -15.81929202

Solving
0.5 + x = -15.81929202

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -15.81929202 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -15.81929202 + -0.5
x = -15.81929202 + -0.5

Combine like terms: -15.81929202 + -0.5 = -16.31929202
x = -16.31929202

Simplifying
x = -16.31929202

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.31929202, -16.31929202}
Solution
x = {15.31929202, -16.31929202}