4y^2-10y=2

Solution for 4y^2-10y=2 equation:

Simplifying
4y2 + -10y = 2

Reorder the terms:
-10y + 4y2 = 2

Solving
-10y + 4y2 = 2

Solving for variable 'y'.

Reorder the terms:
-2 + -10y + 4y2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -10y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -5y + 2y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -5y + 2y2)' equal to zero and attempt to solve:

Simplifying
-1 + -5y + 2y2 = 0

Solving
-1 + -5y + 2y2 = 0

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

Divide each side by '2'.
-0.5 + -2.5y + y2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -2.5y + 0.5 + y2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -2.5y + y2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -2.5y + y2 = 0 + 0.5
-2.5y + y2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-2.5y + y2 = 0.5

The y term is -2.5y.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5y + 1.5625 + y2 = 0.5 + 1.5625

Reorder the terms:
1.5625 + -2.5y + y2 = 0.5 + 1.5625

Combine like terms: 0.5 + 1.5625 = 2.0625
1.5625 + -2.5y + y2 = 2.0625

Factor a perfect square on the left side:
(y + -1.25)(y + -1.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(y + -1.25) equal to 1.436140662 and -1.436140662.

Subproblem 1
y + -1.25 = 1.436140662

Simplifying
y + -1.25 = 1.436140662

Reorder the terms:
-1.25 + y = 1.436140662

Solving
-1.25 + y = 1.436140662

Solving for variable 'y'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + y = 1.436140662 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = 1.436140662 + 1.25
y = 1.436140662 + 1.25

Combine like terms: 1.436140662 + 1.25 = 2.686140662
y = 2.686140662

Simplifying
y = 2.686140662

Subproblem 2
y + -1.25 = -1.436140662

Simplifying
y + -1.25 = -1.436140662

Reorder the terms:
-1.25 + y = -1.436140662

Solving
-1.25 + y = -1.436140662

Solving for variable 'y'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + y = -1.436140662 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = -1.436140662 + 1.25
y = -1.436140662 + 1.25

Combine like terms: -1.436140662 + 1.25 = -0.186140662
y = -0.186140662

Simplifying
y = -0.186140662

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.686140662, -0.186140662}
Solution
y = {2.686140662, -0.186140662}