3y^2+6y-35=0

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Solution for 3y^2+6y-35=0 equation: 


Simplifying
3y2 + 6y + -35 = 0

Reorder the terms:
-35 + 6y + 3y2 = 0

Solving
-35 + 6y + 3y2 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
-11.66666667 + 2y + y2 = 0

Move the constant term to the right:

Add '11.66666667' to each side of the equation.
-11.66666667 + 2y + 11.66666667 + y2 = 0 + 11.66666667

Reorder the terms:
-11.66666667 + 11.66666667 + 2y + y2 = 0 + 11.66666667

Combine like terms: -11.66666667 + 11.66666667 = 0.00000000
0.00000000 + 2y + y2 = 0 + 11.66666667
2y + y2 = 0 + 11.66666667

Combine like terms: 0 + 11.66666667 = 11.66666667
2y + y2 = 11.66666667

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 = 11.66666667 + 1

Reorder the terms:
1 + 2y + y2 = 11.66666667 + 1

Combine like terms: 11.66666667 + 1 = 12.66666667
1 + 2y + y2 = 12.66666667

Factor a perfect square on the left side:
(y + 1)(y + 1) = 12.66666667

Calculate the square root of the right side: 3.559026084

Break this problem into two subproblems by setting 
(y + 1) equal to 3.559026084 and -3.559026084.


Subproblem 1
y + 1 = 3.559026084

Simplifying
y + 1 = 3.559026084

Reorder the terms:
1 + y = 3.559026084

Solving
1 + y = 3.559026084

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 = 3.559026084 + -1

Combine like terms: 1 + -1 = 0
0 + y = 3.559026084 + -1
y = 3.559026084 + -1

Combine like terms: 3.559026084 + -1 = 2.559026084
y = 2.559026084

Simplifying
y = 2.559026084


Subproblem 2
y + 1 = -3.559026084

Simplifying
y + 1 = -3.559026084

Reorder the terms:
1 + y = -3.559026084

Solving
1 + y = -3.559026084

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 = -3.559026084 + -1

Combine like terms: 1 + -1 = 0
0 + y = -3.559026084 + -1
y = -3.559026084 + -1

Combine like terms: -3.559026084 + -1 = -4.559026084
y = -4.559026084

Simplifying
y = -4.559026084


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.559026084, -4.559026084}

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