30y^2-80y-1=0

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Solution for 30y^2-80y-1=0 equation: 


Simplifying
30y2 + -80y + -1 = 0

Reorder the terms:
-1 + -80y + 30y2 = 0

Solving
-1 + -80y + 30y2 = 0

Solving for variable 'y'.

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

Divide each side by '30'.
-0.03333333333 + -2.666666667y + y2 = 0

Move the constant term to the right:

Add '0.03333333333' to each side of the equation.
-0.03333333333 + -2.666666667y + 0.03333333333 + y2 = 0 + 0.03333333333

Reorder the terms:
-0.03333333333 + 0.03333333333 + -2.666666667y + y2 = 0 + 0.03333333333

Combine like terms: -0.03333333333 + 0.03333333333 = 0.00000000000
0.00000000000 + -2.666666667y + y2 = 0 + 0.03333333333
-2.666666667y + y2 = 0 + 0.03333333333

Combine like terms: 0 + 0.03333333333 = 0.03333333333
-2.666666667y + y2 = 0.03333333333

The y term is -2.666666667y.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667y + 1.777777780 + y2 = 0.03333333333 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667y + y2 = 0.03333333333 + 1.777777780

Combine like terms: 0.03333333333 + 1.777777780 = 1.81111111333
1.777777780 + -2.666666667y + y2 = 1.81111111333

Factor a perfect square on the left side:
(y + -1.333333334)(y + -1.333333334) = 1.81111111333

Calculate the square root of the right side: 1.345775283

Break this problem into two subproblems by setting 
(y + -1.333333334) equal to 1.345775283 and -1.345775283.


Subproblem 1
y + -1.333333334 = 1.345775283

Simplifying
y + -1.333333334 = 1.345775283

Reorder the terms:
-1.333333334 + y = 1.345775283

Solving
-1.333333334 + y = 1.345775283

Solving for variable 'y'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + y = 1.345775283 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + y = 1.345775283 + 1.333333334
y = 1.345775283 + 1.333333334

Combine like terms: 1.345775283 + 1.333333334 = 2.679108617
y = 2.679108617

Simplifying
y = 2.679108617


Subproblem 2
y + -1.333333334 = -1.345775283

Simplifying
y + -1.333333334 = -1.345775283

Reorder the terms:
-1.333333334 + y = -1.345775283

Solving
-1.333333334 + y = -1.345775283

Solving for variable 'y'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + y = -1.345775283 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + y = -1.345775283 + 1.333333334
y = -1.345775283 + 1.333333334

Combine like terms: -1.345775283 + 1.333333334 = -0.012441949
y = -0.012441949

Simplifying
y = -0.012441949


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.679108617, -0.012441949}

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