5y^2+4y-4=0

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Solution for 5y^2+4y-4=0 equation: 


Simplifying
5y2 + 4y + -4 = 0

Reorder the terms:
-4 + 4y + 5y2 = 0

Solving
-4 + 4y + 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'.
-0.8 + 0.8y + y2 = 0

Move the constant term to the right:

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

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

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

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

The y term is 0.8y.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8y + 0.16 + y2 = 0.8 + 0.16

Reorder the terms:
0.16 + 0.8y + y2 = 0.8 + 0.16

Combine like terms: 0.8 + 0.16 = 0.96
0.16 + 0.8y + y2 = 0.96

Factor a perfect square on the left side:
(y + 0.4)(y + 0.4) = 0.96

Calculate the square root of the right side: 0.979795897

Break this problem into two subproblems by setting 
(y + 0.4) equal to 0.979795897 and -0.979795897.


Subproblem 1
y + 0.4 = 0.979795897

Simplifying
y + 0.4 = 0.979795897

Reorder the terms:
0.4 + y = 0.979795897

Solving
0.4 + y = 0.979795897

Solving for variable 'y'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + y = 0.979795897 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + y = 0.979795897 + -0.4
y = 0.979795897 + -0.4

Combine like terms: 0.979795897 + -0.4 = 0.579795897
y = 0.579795897

Simplifying
y = 0.579795897


Subproblem 2
y + 0.4 = -0.979795897

Simplifying
y + 0.4 = -0.979795897

Reorder the terms:
0.4 + y = -0.979795897

Solving
0.4 + y = -0.979795897

Solving for variable 'y'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + y = -0.979795897 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + y = -0.979795897 + -0.4
y = -0.979795897 + -0.4

Combine like terms: -0.979795897 + -0.4 = -1.379795897
y = -1.379795897

Simplifying
y = -1.379795897


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.579795897, -1.379795897}

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