-3y^2+30y+25=0

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Solution for -3y^2+30y+25=0 equation: 


Simplifying
-3y2 + 30y + 25 = 0

Reorder the terms:
25 + 30y + -3y2 = 0

Solving
25 + 30y + -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'.
-8.333333333 + -10y + y2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + -10y + 8.333333333 + y2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + -10y + y2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + -10y + y2 = 0 + 8.333333333
-10y + y2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
-10y + y2 = 8.333333333

The y term is -10y.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10y + 25 + y2 = 8.333333333 + 25

Reorder the terms:
25 + -10y + y2 = 8.333333333 + 25

Combine like terms: 8.333333333 + 25 = 33.333333333
25 + -10y + y2 = 33.333333333

Factor a perfect square on the left side:
(y + -5)(y + -5) = 33.333333333

Calculate the square root of the right side: 5.773502692

Break this problem into two subproblems by setting 
(y + -5) equal to 5.773502692 and -5.773502692.


Subproblem 1
y + -5 = 5.773502692

Simplifying
y + -5 = 5.773502692

Reorder the terms:
-5 + y = 5.773502692

Solving
-5 + y = 5.773502692

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + y = 5.773502692 + 5

Combine like terms: -5 + 5 = 0
0 + y = 5.773502692 + 5
y = 5.773502692 + 5

Combine like terms: 5.773502692 + 5 = 10.773502692
y = 10.773502692

Simplifying
y = 10.773502692


Subproblem 2
y + -5 = -5.773502692

Simplifying
y + -5 = -5.773502692

Reorder the terms:
-5 + y = -5.773502692

Solving
-5 + y = -5.773502692

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + y = -5.773502692 + 5

Combine like terms: -5 + 5 = 0
0 + y = -5.773502692 + 5
y = -5.773502692 + 5

Combine like terms: -5.773502692 + 5 = -0.773502692
y = -0.773502692

Simplifying
y = -0.773502692


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.773502692, -0.773502692}

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