5a^2-20a+6=0

Solution for 5a^2-20a+6=0 equation:

Simplifying
5a2 + -20a + 6 = 0

Reorder the terms:
6 + -20a + 5a2 = 0

Solving
6 + -20a + 5a2 = 0

Solving for variable 'a'.

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

Divide each side by '5'.
1.2 + -4a + a2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -4a + -1.2 + a2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -4a + a2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -4a + a2 = 0 + -1.2
-4a + a2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-4a + a2 = -1.2

The a term is -4a.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4a + 4 + a2 = -1.2 + 4

Reorder the terms:
4 + -4a + a2 = -1.2 + 4

Combine like terms: -1.2 + 4 = 2.8
4 + -4a + a2 = 2.8

Factor a perfect square on the left side:
(a + -2)(a + -2) = 2.8

Calculate the square root of the right side: 1.673320053

Break this problem into two subproblems by setting 
(a + -2) equal to 1.673320053 and -1.673320053.

Subproblem 1
a + -2 = 1.673320053

Simplifying
a + -2 = 1.673320053

Reorder the terms:
-2 + a = 1.673320053

Solving
-2 + a = 1.673320053

Solving for variable 'a'.

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

Add '2' to each side of the equation.
-2 + 2 + a = 1.673320053 + 2

Combine like terms: -2 + 2 = 0
0 + a = 1.673320053 + 2
a = 1.673320053 + 2

Combine like terms: 1.673320053 + 2 = 3.673320053
a = 3.673320053

Simplifying
a = 3.673320053

Subproblem 2
a + -2 = -1.673320053

Simplifying
a + -2 = -1.673320053

Reorder the terms:
-2 + a = -1.673320053

Solving
-2 + a = -1.673320053

Solving for variable 'a'.

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

Add '2' to each side of the equation.
-2 + 2 + a = -1.673320053 + 2

Combine like terms: -2 + 2 = 0
0 + a = -1.673320053 + 2
a = -1.673320053 + 2

Combine like terms: -1.673320053 + 2 = 0.326679947
a = 0.326679947

Simplifying
a = 0.326679947

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.673320053, 0.326679947}