1.3y(y-0.5)=0.3(y+17)

Solution for 1.3y(y-0.5)=0.3(y+17) equation:

Simplifying
1.3y(y + -0.5) = 0.3(y + 17)

Reorder the terms:
1.3y(-0.5 + y) = 0.3(y + 17)
(-0.5 * 1.3y + y * 1.3y) = 0.3(y + 17)
(-0.65y + 1.3y2) = 0.3(y + 17)

Reorder the terms:
-0.65y + 1.3y2 = 0.3(17 + y)
-0.65y + 1.3y2 = (17 * 0.3 + y * 0.3)
-0.65y + 1.3y2 = (5.1 + 0.3y)

Solving
-0.65y + 1.3y2 = 5.1 + 0.3y

Solving for variable 'y'.

Reorder the terms:
-5.1 + -0.65y + -0.3y + 1.3y2 = 5.1 + 0.3y + -5.1 + -0.3y

Combine like terms: -0.65y + -0.3y = -0.95y
-5.1 + -0.95y + 1.3y2 = 5.1 + 0.3y + -5.1 + -0.3y

Reorder the terms:
-5.1 + -0.95y + 1.3y2 = 5.1 + -5.1 + 0.3y + -0.3y

Combine like terms: 5.1 + -5.1 = 0.0
-5.1 + -0.95y + 1.3y2 = 0.0 + 0.3y + -0.3y
-5.1 + -0.95y + 1.3y2 = 0.3y + -0.3y

Combine like terms: 0.3y + -0.3y = 0.0
-5.1 + -0.95y + 1.3y2 = 0.0

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

Divide each side by '1.3'.
-3.923076923 + -0.7307692308y + y2 = 0

Move the constant term to the right:

Add '3.923076923' to each side of the equation.
-3.923076923 + -0.7307692308y + 3.923076923 + y2 = 0 + 3.923076923

Reorder the terms:
-3.923076923 + 3.923076923 + -0.7307692308y + y2 = 0 + 3.923076923

Combine like terms: -3.923076923 + 3.923076923 = 0.000000000
0.000000000 + -0.7307692308y + y2 = 0 + 3.923076923
-0.7307692308y + y2 = 0 + 3.923076923

Combine like terms: 0 + 3.923076923 = 3.923076923
-0.7307692308y + y2 = 3.923076923

The y term is -0.7307692308y.  Take half its coefficient (-0.3653846154).
Square it (0.1335059172) and add it to both sides.

Add '0.1335059172' to each side of the equation.
-0.7307692308y + 0.1335059172 + y2 = 3.923076923 + 0.1335059172

Reorder the terms:
0.1335059172 + -0.7307692308y + y2 = 3.923076923 + 0.1335059172

Combine like terms: 3.923076923 + 0.1335059172 = 4.0565828402
0.1335059172 + -0.7307692308y + y2 = 4.0565828402

Factor a perfect square on the left side:
(y + -0.3653846154)(y + -0.3653846154) = 4.0565828402

Calculate the square root of the right side: 2.014096035

Break this problem into two subproblems by setting 
(y + -0.3653846154) equal to 2.014096035 and -2.014096035.

Subproblem 1
y + -0.3653846154 = 2.014096035

Simplifying
y + -0.3653846154 = 2.014096035

Reorder the terms:
-0.3653846154 + y = 2.014096035

Solving
-0.3653846154 + y = 2.014096035

Solving for variable 'y'.

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

Add '0.3653846154' to each side of the equation.
-0.3653846154 + 0.3653846154 + y = 2.014096035 + 0.3653846154

Combine like terms: -0.3653846154 + 0.3653846154 = 0.0000000000
0.0000000000 + y = 2.014096035 + 0.3653846154
y = 2.014096035 + 0.3653846154

Combine like terms: 2.014096035 + 0.3653846154 = 2.3794806504
y = 2.3794806504

Simplifying
y = 2.3794806504

Subproblem 2
y + -0.3653846154 = -2.014096035

Simplifying
y + -0.3653846154 = -2.014096035

Reorder the terms:
-0.3653846154 + y = -2.014096035

Solving
-0.3653846154 + y = -2.014096035

Solving for variable 'y'.

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

Add '0.3653846154' to each side of the equation.
-0.3653846154 + 0.3653846154 + y = -2.014096035 + 0.3653846154

Combine like terms: -0.3653846154 + 0.3653846154 = 0.0000000000
0.0000000000 + y = -2.014096035 + 0.3653846154
y = -2.014096035 + 0.3653846154

Combine like terms: -2.014096035 + 0.3653846154 = -1.6487114196
y = -1.6487114196

Simplifying
y = -1.6487114196

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.3794806504, -1.6487114196}