2y^2+4y-9=0

Solution for 2y^2+4y-9=0 equation:

Simplifying
2y2 + 4y + -9 = 0

Reorder the terms:
-9 + 4y + 2y2 = 0

Solving
-9 + 4y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
-4.5 + 2y + y2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + 2y + 4.5 + y2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + 2y + y2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + 2y + y2 = 0 + 4.5
2y + y2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
2y + y2 = 4.5

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 = 4.5 + 1

Reorder the terms:
1 + 2y + y2 = 4.5 + 1

Combine like terms: 4.5 + 1 = 5.5
1 + 2y + y2 = 5.5

Factor a perfect square on the left side:
(y + 1)(y + 1) = 5.5

Calculate the square root of the right side: 2.34520788

Break this problem into two subproblems by setting 
(y + 1) equal to 2.34520788 and -2.34520788.

Subproblem 1
y + 1 = 2.34520788

Simplifying
y + 1 = 2.34520788

Reorder the terms:
1 + y = 2.34520788

Solving
1 + y = 2.34520788

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 = 2.34520788 + -1

Combine like terms: 1 + -1 = 0
0 + y = 2.34520788 + -1
y = 2.34520788 + -1

Combine like terms: 2.34520788 + -1 = 1.34520788
y = 1.34520788

Simplifying
y = 1.34520788

Subproblem 2
y + 1 = -2.34520788

Simplifying
y + 1 = -2.34520788

Reorder the terms:
1 + y = -2.34520788

Solving
1 + y = -2.34520788

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 = -2.34520788 + -1

Combine like terms: 1 + -1 = 0
0 + y = -2.34520788 + -1
y = -2.34520788 + -1

Combine like terms: -2.34520788 + -1 = -3.34520788
y = -3.34520788

Simplifying
y = -3.34520788

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.34520788, -3.34520788}