0.0003x^2-4x+0.2=0

Solution for 0.0003x^2-4x+0.2=0 equation:

Simplifying
0.0003x2 + -4x + 0.2 = 0

Reorder the terms:
0.2 + -4x + 0.0003x2 = 0

Solving
0.2 + -4x + 0.0003x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.0003 the coefficient of the squared term: 

Divide each side by '0.0003'.
666.6666667 + -13333.33333x + x2 = 0

Move the constant term to the right:

Add '-666.6666667' to each side of the equation.
666.6666667 + -13333.33333x + -666.6666667 + x2 = 0 + -666.6666667

Reorder the terms:
666.6666667 + -666.6666667 + -13333.33333x + x2 = 0 + -666.6666667

Combine like terms: 666.6666667 + -666.6666667 = 0.0000000
0.0000000 + -13333.33333x + x2 = 0 + -666.6666667
-13333.33333x + x2 = 0 + -666.6666667

Combine like terms: 0 + -666.6666667 = -666.6666667
-13333.33333x + x2 = -666.6666667

The x term is -13333.33333x.  Take half its coefficient (-6666.666665).
Square it (44444444.42) and add it to both sides.

Add '44444444.42' to each side of the equation.
-13333.33333x + 44444444.42 + x2 = -666.6666667 + 44444444.42

Reorder the terms:
44444444.42 + -13333.33333x + x2 = -666.6666667 + 44444444.42

Combine like terms: -666.6666667 + 44444444.42 = 44443777.7533333
44444444.42 + -13333.33333x + x2 = 44443777.7533333

Factor a perfect square on the left side:
(x + -6666.666665)(x + -6666.666665) = 44443777.7533333

Calculate the square root of the right side: 6666.616664646

Break this problem into two subproblems by setting 
(x + -6666.666665) equal to 6666.616664646 and -6666.616664646.

Subproblem 1
x + -6666.666665 = 6666.616664646

Simplifying
x + -6666.666665 = 6666.616664646

Reorder the terms:
-6666.666665 + x = 6666.616664646

Solving
-6666.666665 + x = 6666.616664646

Solving for variable 'x'.

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

Add '6666.666665' to each side of the equation.
-6666.666665 + 6666.666665 + x = 6666.616664646 + 6666.666665

Combine like terms: -6666.666665 + 6666.666665 = 0.000000
0.000000 + x = 6666.616664646 + 6666.666665
x = 6666.616664646 + 6666.666665

Combine like terms: 6666.616664646 + 6666.666665 = 13333.283329646
x = 13333.283329646

Simplifying
x = 13333.283329646

Subproblem 2
x + -6666.666665 = -6666.616664646

Simplifying
x + -6666.666665 = -6666.616664646

Reorder the terms:
-6666.666665 + x = -6666.616664646

Solving
-6666.666665 + x = -6666.616664646

Solving for variable 'x'.

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

Add '6666.666665' to each side of the equation.
-6666.666665 + 6666.666665 + x = -6666.616664646 + 6666.666665

Combine like terms: -6666.666665 + 6666.666665 = 0.000000
0.000000 + x = -6666.616664646 + 6666.666665
x = -6666.616664646 + 6666.666665

Combine like terms: -6666.616664646 + 6666.666665 = 0.050000354
x = 0.050000354

Simplifying
x = 0.050000354

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13333.283329646, 0.050000354}