4.9x^2-16x+6=0

Solution for 4.9x^2-16x+6=0 equation:

Simplifying
4.9x2 + -16x + 6 = 0

Reorder the terms:
6 + -16x + 4.9x2 = 0

Solving
6 + -16x + 4.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.9'.
1.224489796 + -3.265306122x + x2 = 0

Move the constant term to the right:

Add '-1.224489796' to each side of the equation.
1.224489796 + -3.265306122x + -1.224489796 + x2 = 0 + -1.224489796

Reorder the terms:
1.224489796 + -1.224489796 + -3.265306122x + x2 = 0 + -1.224489796

Combine like terms: 1.224489796 + -1.224489796 = 0.000000000
0.000000000 + -3.265306122x + x2 = 0 + -1.224489796
-3.265306122x + x2 = 0 + -1.224489796

Combine like terms: 0 + -1.224489796 = -1.224489796
-3.265306122x + x2 = -1.224489796

The x term is -3.265306122x.  Take half its coefficient (-1.632653061).
Square it (2.665556018) and add it to both sides.

Add '2.665556018' to each side of the equation.
-3.265306122x + 2.665556018 + x2 = -1.224489796 + 2.665556018

Reorder the terms:
2.665556018 + -3.265306122x + x2 = -1.224489796 + 2.665556018

Combine like terms: -1.224489796 + 2.665556018 = 1.441066222
2.665556018 + -3.265306122x + x2 = 1.441066222

Factor a perfect square on the left side:
(x + -1.632653061)(x + -1.632653061) = 1.441066222

Calculate the square root of the right side: 1.200444177

Break this problem into two subproblems by setting 
(x + -1.632653061) equal to 1.200444177 and -1.200444177.

Subproblem 1
x + -1.632653061 = 1.200444177

Simplifying
x + -1.632653061 = 1.200444177

Reorder the terms:
-1.632653061 + x = 1.200444177

Solving
-1.632653061 + x = 1.200444177

Solving for variable 'x'.

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

Add '1.632653061' to each side of the equation.
-1.632653061 + 1.632653061 + x = 1.200444177 + 1.632653061

Combine like terms: -1.632653061 + 1.632653061 = 0.000000000
0.000000000 + x = 1.200444177 + 1.632653061
x = 1.200444177 + 1.632653061

Combine like terms: 1.200444177 + 1.632653061 = 2.833097238
x = 2.833097238

Simplifying
x = 2.833097238

Subproblem 2
x + -1.632653061 = -1.200444177

Simplifying
x + -1.632653061 = -1.200444177

Reorder the terms:
-1.632653061 + x = -1.200444177

Solving
-1.632653061 + x = -1.200444177

Solving for variable 'x'.

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

Add '1.632653061' to each side of the equation.
-1.632653061 + 1.632653061 + x = -1.200444177 + 1.632653061

Combine like terms: -1.632653061 + 1.632653061 = 0.000000000
0.000000000 + x = -1.200444177 + 1.632653061
x = -1.200444177 + 1.632653061

Combine like terms: -1.200444177 + 1.632653061 = 0.432208884
x = 0.432208884

Simplifying
x = 0.432208884

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.833097238, 0.432208884}