5y^2-10y=4

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Solution for 5y^2-10y=4 equation: 


Simplifying
5y2 + -10y = 4

Reorder the terms:
-10y + 5y2 = 4

Solving
-10y + 5y2 = 4

Solving for variable 'y'.

Reorder the terms:
-4 + -10y + 5y2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -10y + 5y2 = 0

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

Divide each side by '5'.
-0.8 + -2y + y2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -2y + 0.8 + y2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -2y + y2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -2y + y2 = 0 + 0.8
-2y + y2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-2y + y2 = 0.8

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 = 0.8 + 1

Reorder the terms:
1 + -2y + y2 = 0.8 + 1

Combine like terms: 0.8 + 1 = 1.8
1 + -2y + y2 = 1.8

Factor a perfect square on the left side:
(y + -1)(y + -1) = 1.8

Calculate the square root of the right side: 1.341640787

Break this problem into two subproblems by setting 
(y + -1) equal to 1.341640787 and -1.341640787.


Subproblem 1
y + -1 = 1.341640787

Simplifying
y + -1 = 1.341640787

Reorder the terms:
-1 + y = 1.341640787

Solving
-1 + y = 1.341640787

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 = 1.341640787 + 1

Combine like terms: -1 + 1 = 0
0 + y = 1.341640787 + 1
y = 1.341640787 + 1

Combine like terms: 1.341640787 + 1 = 2.341640787
y = 2.341640787

Simplifying
y = 2.341640787


Subproblem 2
y + -1 = -1.341640787

Simplifying
y + -1 = -1.341640787

Reorder the terms:
-1 + y = -1.341640787

Solving
-1 + y = -1.341640787

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 = -1.341640787 + 1

Combine like terms: -1 + 1 = 0
0 + y = -1.341640787 + 1
y = -1.341640787 + 1

Combine like terms: -1.341640787 + 1 = -0.341640787
y = -0.341640787

Simplifying
y = -0.341640787


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.341640787, -0.341640787}

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