10x^2-51x+6=0

Solution for 10x^2-51x+6=0 equation:

Simplifying
10x2 + -51x + 6 = 0

Reorder the terms:
6 + -51x + 10x2 = 0

Solving
6 + -51x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
0.6 + -5.1x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -5.1x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -5.1x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -5.1x + x2 = 0 + -0.6
-5.1x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-5.1x + x2 = -0.6

The x term is -5.1x.  Take half its coefficient (-2.55).
Square it (6.5025) and add it to both sides.

Add '6.5025' to each side of the equation.
-5.1x + 6.5025 + x2 = -0.6 + 6.5025

Reorder the terms:
6.5025 + -5.1x + x2 = -0.6 + 6.5025

Combine like terms: -0.6 + 6.5025 = 5.9025
6.5025 + -5.1x + x2 = 5.9025

Factor a perfect square on the left side:
(x + -2.55)(x + -2.55) = 5.9025

Calculate the square root of the right side: 2.429506123

Break this problem into two subproblems by setting 
(x + -2.55) equal to 2.429506123 and -2.429506123.

Subproblem 1
x + -2.55 = 2.429506123

Simplifying
x + -2.55 = 2.429506123

Reorder the terms:
-2.55 + x = 2.429506123

Solving
-2.55 + x = 2.429506123

Solving for variable 'x'.

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

Add '2.55' to each side of the equation.
-2.55 + 2.55 + x = 2.429506123 + 2.55

Combine like terms: -2.55 + 2.55 = 0.00
0.00 + x = 2.429506123 + 2.55
x = 2.429506123 + 2.55

Combine like terms: 2.429506123 + 2.55 = 4.979506123
x = 4.979506123

Simplifying
x = 4.979506123

Subproblem 2
x + -2.55 = -2.429506123

Simplifying
x + -2.55 = -2.429506123

Reorder the terms:
-2.55 + x = -2.429506123

Solving
-2.55 + x = -2.429506123

Solving for variable 'x'.

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

Add '2.55' to each side of the equation.
-2.55 + 2.55 + x = -2.429506123 + 2.55

Combine like terms: -2.55 + 2.55 = 0.00
0.00 + x = -2.429506123 + 2.55
x = -2.429506123 + 2.55

Combine like terms: -2.429506123 + 2.55 = 0.120493877
x = 0.120493877

Simplifying
x = 0.120493877

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.979506123, 0.120493877}