17a(a-1)=34(3a-5.6)

Solution for 17a(a-1)=34(3a-5.6) equation:

Simplifying
17a(a + -1) = 34(3a + -5.6)

Reorder the terms:
17a(-1 + a) = 34(3a + -5.6)
(-1 * 17a + a * 17a) = 34(3a + -5.6)
(-17a + 17a2) = 34(3a + -5.6)

Reorder the terms:
-17a + 17a2 = 34(-5.6 + 3a)
-17a + 17a2 = (-5.6 * 34 + 3a * 34)
-17a + 17a2 = (-190.4 + 102a)

Solving
-17a + 17a2 = -190.4 + 102a

Solving for variable 'a'.

Reorder the terms:
190.4 + -17a + -102a + 17a2 = -190.4 + 102a + 190.4 + -102a

Combine like terms: -17a + -102a = -119a
190.4 + -119a + 17a2 = -190.4 + 102a + 190.4 + -102a

Reorder the terms:
190.4 + -119a + 17a2 = -190.4 + 190.4 + 102a + -102a

Combine like terms: -190.4 + 190.4 = 0.0
190.4 + -119a + 17a2 = 0.0 + 102a + -102a
190.4 + -119a + 17a2 = 102a + -102a

Combine like terms: 102a + -102a = 0
190.4 + -119a + 17a2 = 0

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

Divide each side by '17'.
11.2 + -7a + a2 = 0

Move the constant term to the right:

Add '-11.2' to each side of the equation.
11.2 + -7a + -11.2 + a2 = 0 + -11.2

Reorder the terms:
11.2 + -11.2 + -7a + a2 = 0 + -11.2

Combine like terms: 11.2 + -11.2 = 0.0
0.0 + -7a + a2 = 0 + -11.2
-7a + a2 = 0 + -11.2

Combine like terms: 0 + -11.2 = -11.2
-7a + a2 = -11.2

The a term is -7a.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7a + 12.25 + a2 = -11.2 + 12.25

Reorder the terms:
12.25 + -7a + a2 = -11.2 + 12.25

Combine like terms: -11.2 + 12.25 = 1.05
12.25 + -7a + a2 = 1.05

Factor a perfect square on the left side:
(a + -3.5)(a + -3.5) = 1.05

Calculate the square root of the right side: 1.024695077

Break this problem into two subproblems by setting 
(a + -3.5) equal to 1.024695077 and -1.024695077.

Subproblem 1
a + -3.5 = 1.024695077

Simplifying
a + -3.5 = 1.024695077

Reorder the terms:
-3.5 + a = 1.024695077

Solving
-3.5 + a = 1.024695077

Solving for variable 'a'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + a = 1.024695077 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + a = 1.024695077 + 3.5
a = 1.024695077 + 3.5

Combine like terms: 1.024695077 + 3.5 = 4.524695077
a = 4.524695077

Simplifying
a = 4.524695077

Subproblem 2
a + -3.5 = -1.024695077

Simplifying
a + -3.5 = -1.024695077

Reorder the terms:
-3.5 + a = -1.024695077

Solving
-3.5 + a = -1.024695077

Solving for variable 'a'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + a = -1.024695077 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + a = -1.024695077 + 3.5
a = -1.024695077 + 3.5

Combine like terms: -1.024695077 + 3.5 = 2.475304923
a = 2.475304923

Simplifying
a = 2.475304923

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.524695077, 2.475304923}