.06x^2-48x+6=0

Solution for .06x^2-48x+6=0 equation:

Simplifying
0.06x2 + -48x + 6 = 0

Reorder the terms:
6 + -48x + 0.06x2 = 0

Solving
6 + -48x + 0.06x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.06'.
100 + -800x + x2 = 0

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -800x + -100 + x2 = 0 + -100

Reorder the terms:
100 + -100 + -800x + x2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -800x + x2 = 0 + -100
-800x + x2 = 0 + -100

Combine like terms: 0 + -100 = -100
-800x + x2 = -100

The x term is -800x.  Take half its coefficient (-400).
Square it (160000) and add it to both sides.

Add '160000' to each side of the equation.
-800x + 160000 + x2 = -100 + 160000

Reorder the terms:
160000 + -800x + x2 = -100 + 160000

Combine like terms: -100 + 160000 = 159900
160000 + -800x + x2 = 159900

Factor a perfect square on the left side:
(x + -400)(x + -400) = 159900

Calculate the square root of the right side: 399.874980463

Break this problem into two subproblems by setting 
(x + -400) equal to 399.874980463 and -399.874980463.

Subproblem 1
x + -400 = 399.874980463

Simplifying
x + -400 = 399.874980463

Reorder the terms:
-400 + x = 399.874980463

Solving
-400 + x = 399.874980463

Solving for variable 'x'.

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

Add '400' to each side of the equation.
-400 + 400 + x = 399.874980463 + 400

Combine like terms: -400 + 400 = 0
0 + x = 399.874980463 + 400
x = 399.874980463 + 400

Combine like terms: 399.874980463 + 400 = 799.874980463
x = 799.874980463

Simplifying
x = 799.874980463

Subproblem 2
x + -400 = -399.874980463

Simplifying
x + -400 = -399.874980463

Reorder the terms:
-400 + x = -399.874980463

Solving
-400 + x = -399.874980463

Solving for variable 'x'.

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

Add '400' to each side of the equation.
-400 + 400 + x = -399.874980463 + 400

Combine like terms: -400 + 400 = 0
0 + x = -399.874980463 + 400
x = -399.874980463 + 400

Combine like terms: -399.874980463 + 400 = 0.125019537
x = 0.125019537

Simplifying
x = 0.125019537

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {799.874980463, 0.125019537}