5y^2-10y+3=0

Solution for 5y^2-10y+3=0 equation:

Simplifying
5y2 + -10y + 3 = 0

Reorder the terms:
3 + -10y + 5y2 = 0

Solving
3 + -10y + 5y2 = 0

Solving for variable 'y'.

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

Divide each side by '5'.
0.6 + -2y + y2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -2y + -0.6 + y2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -2y + y2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -2y + y2 = 0 + -0.6
-2y + y2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-2y + y2 = -0.6

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = -0.6 + 1

Reorder the terms:
1 + -2y + y2 = -0.6 + 1

Combine like terms: -0.6 + 1 = 0.4
1 + -2y + y2 = 0.4

Factor a perfect square on the left side:
(y + -1)(y + -1) = 0.4

Calculate the square root of the right side: 0.632455532

Break this problem into two subproblems by setting 
(y + -1) equal to 0.632455532 and -0.632455532.

Subproblem 1
y + -1 = 0.632455532

Simplifying
y + -1 = 0.632455532

Reorder the terms:
-1 + y = 0.632455532

Solving
-1 + y = 0.632455532

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = 0.632455532 + 1

Combine like terms: -1 + 1 = 0
0 + y = 0.632455532 + 1
y = 0.632455532 + 1

Combine like terms: 0.632455532 + 1 = 1.632455532
y = 1.632455532

Simplifying
y = 1.632455532

Subproblem 2
y + -1 = -0.632455532

Simplifying
y + -1 = -0.632455532

Reorder the terms:
-1 + y = -0.632455532

Solving
-1 + y = -0.632455532

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = -0.632455532 + 1

Combine like terms: -1 + 1 = 0
0 + y = -0.632455532 + 1
y = -0.632455532 + 1

Combine like terms: -0.632455532 + 1 = 0.367544468
y = 0.367544468

Simplifying
y = 0.367544468

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.632455532, 0.367544468}