680000=2x^2+-2000x+1000000

Solution for 680000=2x^2+-2000x+1000000 equation:

Simplifying
680000 = 2x2 + -2000x + 1000000

Reorder the terms:
680000 = 1000000 + -2000x + 2x2

Solving
680000 = 1000000 + -2000x + 2x2

Solving for variable 'x'.

Combine like terms: 680000 + -1000000 = -320000
-320000 + 2000x + -2x2 = 1000000 + -2000x + 2x2 + -1000000 + 2000x + -2x2

Reorder the terms:
-320000 + 2000x + -2x2 = 1000000 + -1000000 + -2000x + 2000x + 2x2 + -2x2

Combine like terms: 1000000 + -1000000 = 0
-320000 + 2000x + -2x2 = 0 + -2000x + 2000x + 2x2 + -2x2
-320000 + 2000x + -2x2 = -2000x + 2000x + 2x2 + -2x2

Combine like terms: -2000x + 2000x = 0
-320000 + 2000x + -2x2 = 0 + 2x2 + -2x2
-320000 + 2000x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-320000 + 2000x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-160000 + 1000x + -1x2) = 0

Factor a trinomial.
2((-800 + x)(200 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-800 + x)' equal to zero and attempt to solve:

Simplifying
-800 + x = 0

Solving
-800 + x = 0

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

Add '800' to each side of the equation.
-800 + 800 + x = 0 + 800

Combine like terms: -800 + 800 = 0
0 + x = 0 + 800
x = 0 + 800

Combine like terms: 0 + 800 = 800
x = 800

Simplifying
x = 800
Subproblem 2
Set the factor '(200 + -1x)' equal to zero and attempt to solve:

Simplifying
200 + -1x = 0

Solving
200 + -1x = 0

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

Add '-200' to each side of the equation.
200 + -200 + -1x = 0 + -200

Combine like terms: 200 + -200 = 0
0 + -1x = 0 + -200
-1x = 0 + -200

Combine like terms: 0 + -200 = -200
-1x = -200

Divide each side by '-1'.
x = 200

Simplifying
x = 200
Solution
x = {800, 200}