5y^2-15y+2=10

Solution for 5y^2-15y+2=10 equation:

Simplifying
5y2 + -15y + 2 = 10

Reorder the terms:
2 + -15y + 5y2 = 10

Solving
2 + -15y + 5y2 = 10

Solving for variable 'y'.

Reorder the terms:
2 + -10 + -15y + 5y2 = 10 + -10

Combine like terms: 2 + -10 = -8
-8 + -15y + 5y2 = 10 + -10

Combine like terms: 10 + -10 = 0
-8 + -15y + 5y2 = 0

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

Divide each side by '5'.
-1.6 + -3y + y2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -3y + 1.6 + y2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -3y + y2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -3y + y2 = 0 + 1.6
-3y + y2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-3y + y2 = 1.6

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 1.6 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 1.6 + 2.25

Combine like terms: 1.6 + 2.25 = 3.85
2.25 + -3y + y2 = 3.85

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 3.85

Calculate the square root of the right side: 1.962141687

Break this problem into two subproblems by setting 
(y + -1.5) equal to 1.962141687 and -1.962141687.

Subproblem 1
y + -1.5 = 1.962141687

Simplifying
y + -1.5 = 1.962141687

Reorder the terms:
-1.5 + y = 1.962141687

Solving
-1.5 + y = 1.962141687

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 1.962141687 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 1.962141687 + 1.5
y = 1.962141687 + 1.5

Combine like terms: 1.962141687 + 1.5 = 3.462141687
y = 3.462141687

Simplifying
y = 3.462141687

Subproblem 2
y + -1.5 = -1.962141687

Simplifying
y + -1.5 = -1.962141687

Reorder the terms:
-1.5 + y = -1.962141687

Solving
-1.5 + y = -1.962141687

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -1.962141687 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -1.962141687 + 1.5
y = -1.962141687 + 1.5

Combine like terms: -1.962141687 + 1.5 = -0.462141687
y = -0.462141687

Simplifying
y = -0.462141687

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.462141687, -0.462141687}