3y^2+45y-6500=0

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Solution for 3y^2+45y-6500=0 equation: 


Simplifying
3y2 + 45y + -6500 = 0

Reorder the terms:
-6500 + 45y + 3y2 = 0

Solving
-6500 + 45y + 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'.
-2166.666667 + 15y + y2 = 0

Move the constant term to the right:

Add '2166.666667' to each side of the equation.
-2166.666667 + 15y + 2166.666667 + y2 = 0 + 2166.666667

Reorder the terms:
-2166.666667 + 2166.666667 + 15y + y2 = 0 + 2166.666667

Combine like terms: -2166.666667 + 2166.666667 = 0.000000
0.000000 + 15y + y2 = 0 + 2166.666667
15y + y2 = 0 + 2166.666667

Combine like terms: 0 + 2166.666667 = 2166.666667
15y + y2 = 2166.666667

The y term is 15y.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15y + 56.25 + y2 = 2166.666667 + 56.25

Reorder the terms:
56.25 + 15y + y2 = 2166.666667 + 56.25

Combine like terms: 2166.666667 + 56.25 = 2222.916667
56.25 + 15y + y2 = 2222.916667

Factor a perfect square on the left side:
(y + 7.5)(y + 7.5) = 2222.916667

Calculate the square root of the right side: 47.147817203

Break this problem into two subproblems by setting 
(y + 7.5) equal to 47.147817203 and -47.147817203.


Subproblem 1
y + 7.5 = 47.147817203

Simplifying
y + 7.5 = 47.147817203

Reorder the terms:
7.5 + y = 47.147817203

Solving
7.5 + y = 47.147817203

Solving for variable 'y'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + y = 47.147817203 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + y = 47.147817203 + -7.5
y = 47.147817203 + -7.5

Combine like terms: 47.147817203 + -7.5 = 39.647817203
y = 39.647817203

Simplifying
y = 39.647817203


Subproblem 2
y + 7.5 = -47.147817203

Simplifying
y + 7.5 = -47.147817203

Reorder the terms:
7.5 + y = -47.147817203

Solving
7.5 + y = -47.147817203

Solving for variable 'y'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + y = -47.147817203 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + y = -47.147817203 + -7.5
y = -47.147817203 + -7.5

Combine like terms: -47.147817203 + -7.5 = -54.647817203
y = -54.647817203

Simplifying
y = -54.647817203


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {39.647817203, -54.647817203}

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