7x^2+6-7000x=0

Solution for 7x^2+6-7000x=0 equation:

Simplifying
7x2 + 6 + -7000x = 0

Reorder the terms:
6 + -7000x + 7x2 = 0

Solving
6 + -7000x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
0.8571428571 + -1000x + x2 = 0

Move the constant term to the right:

Add '-0.8571428571' to each side of the equation.
0.8571428571 + -1000x + -0.8571428571 + x2 = 0 + -0.8571428571

Reorder the terms:
0.8571428571 + -0.8571428571 + -1000x + x2 = 0 + -0.8571428571

Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000
0.0000000000 + -1000x + x2 = 0 + -0.8571428571
-1000x + x2 = 0 + -0.8571428571

Combine like terms: 0 + -0.8571428571 = -0.8571428571
-1000x + x2 = -0.8571428571

The x term is -1000x.  Take half its coefficient (-500).
Square it (250000) and add it to both sides.

Add '250000' to each side of the equation.
-1000x + 250000 + x2 = -0.8571428571 + 250000

Reorder the terms:
250000 + -1000x + x2 = -0.8571428571 + 250000

Combine like terms: -0.8571428571 + 250000 = 249999.1428571429
250000 + -1000x + x2 = 249999.1428571429

Factor a perfect square on the left side:
(x + -500)(x + -500) = 249999.1428571429

Calculate the square root of the right side: 499.999142856

Break this problem into two subproblems by setting 
(x + -500) equal to 499.999142856 and -499.999142856.

Subproblem 1
x + -500 = 499.999142856

Simplifying
x + -500 = 499.999142856

Reorder the terms:
-500 + x = 499.999142856

Solving
-500 + x = 499.999142856

Solving for variable 'x'.

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

Add '500' to each side of the equation.
-500 + 500 + x = 499.999142856 + 500

Combine like terms: -500 + 500 = 0
0 + x = 499.999142856 + 500
x = 499.999142856 + 500

Combine like terms: 499.999142856 + 500 = 999.999142856
x = 999.999142856

Simplifying
x = 999.999142856

Subproblem 2
x + -500 = -499.999142856

Simplifying
x + -500 = -499.999142856

Reorder the terms:
-500 + x = -499.999142856

Solving
-500 + x = -499.999142856

Solving for variable 'x'.

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

Add '500' to each side of the equation.
-500 + 500 + x = -499.999142856 + 500

Combine like terms: -500 + 500 = 0
0 + x = -499.999142856 + 500
x = -499.999142856 + 500

Combine like terms: -499.999142856 + 500 = 0.000857144
x = 0.000857144

Simplifying
x = 0.000857144

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {999.999142856, 0.000857144}