3y^2+y=94

Solution for 3y^2+y=94 equation:

Simplifying
3y2 + y = 94

Reorder the terms:
y + 3y2 = 94

Solving
y + 3y2 = 94

Solving for variable 'y'.

Reorder the terms:
-94 + y + 3y2 = 94 + -94

Combine like terms: 94 + -94 = 0
-94 + y + 3y2 = 0

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

Divide each side by '3'.
-31.33333333 + 0.3333333333y + y2 = 0

Move the constant term to the right:

Add '31.33333333' to each side of the equation.
-31.33333333 + 0.3333333333y + 31.33333333 + y2 = 0 + 31.33333333

Reorder the terms:
-31.33333333 + 31.33333333 + 0.3333333333y + y2 = 0 + 31.33333333

Combine like terms: -31.33333333 + 31.33333333 = 0.00000000
0.00000000 + 0.3333333333y + y2 = 0 + 31.33333333
0.3333333333y + y2 = 0 + 31.33333333

Combine like terms: 0 + 31.33333333 = 31.33333333
0.3333333333y + y2 = 31.33333333

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333y + 0.25 + y2 = 31.33333333 + 0.25

Reorder the terms:
0.25 + 0.3333333333y + y2 = 31.33333333 + 0.25

Combine like terms: 31.33333333 + 0.25 = 31.58333333
0.25 + 0.3333333333y + y2 = 31.58333333

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 31.58333333

Calculate the square root of the right side: 5.6199051

Break this problem into two subproblems by setting 
(y + 0.5) equal to 5.6199051 and -5.6199051.

Subproblem 1
y + 0.5 = 5.6199051

Simplifying
y + 0.5 = 5.6199051

Reorder the terms:
0.5 + y = 5.6199051

Solving
0.5 + y = 5.6199051

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 5.6199051 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 5.6199051 + -0.5
y = 5.6199051 + -0.5

Combine like terms: 5.6199051 + -0.5 = 5.1199051
y = 5.1199051

Simplifying
y = 5.1199051

Subproblem 2
y + 0.5 = -5.6199051

Simplifying
y + 0.5 = -5.6199051

Reorder the terms:
0.5 + y = -5.6199051

Solving
0.5 + y = -5.6199051

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -5.6199051 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -5.6199051 + -0.5
y = -5.6199051 + -0.5

Combine like terms: -5.6199051 + -0.5 = -6.1199051
y = -6.1199051

Simplifying
y = -6.1199051

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.1199051, -6.1199051}