6y^2+17y-5=0

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Solution for 6y^2+17y-5=0 equation: 


Simplifying
6y2 + 17y + -5 = 0

Reorder the terms:
-5 + 17y + 6y2 = 0

Solving
-5 + 17y + 6y2 = 0

Solving for variable 'y'.

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

Divide each side by '6'.
-0.8333333333 + 2.833333333y + y2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + 2.833333333y + 0.8333333333 + y2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + 2.833333333y + y2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + 2.833333333y + y2 = 0 + 0.8333333333
2.833333333y + y2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
2.833333333y + y2 = 0.8333333333

The y term is 2.833333333y.  Take half its coefficient (1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
2.833333333y + 2.006944445 + y2 = 0.8333333333 + 2.006944445

Reorder the terms:
2.006944445 + 2.833333333y + y2 = 0.8333333333 + 2.006944445

Combine like terms: 0.8333333333 + 2.006944445 = 2.8402777783
2.006944445 + 2.833333333y + y2 = 2.8402777783

Factor a perfect square on the left side:
(y + 1.416666667)(y + 1.416666667) = 2.8402777783

Calculate the square root of the right side: 1.685312368

Break this problem into two subproblems by setting 
(y + 1.416666667) equal to 1.685312368 and -1.685312368.


Subproblem 1
y + 1.416666667 = 1.685312368

Simplifying
y + 1.416666667 = 1.685312368

Reorder the terms:
1.416666667 + y = 1.685312368

Solving
1.416666667 + y = 1.685312368

Solving for variable 'y'.

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

Add '-1.416666667' to each side of the equation.
1.416666667 + -1.416666667 + y = 1.685312368 + -1.416666667

Combine like terms: 1.416666667 + -1.416666667 = 0.000000000
0.000000000 + y = 1.685312368 + -1.416666667
y = 1.685312368 + -1.416666667

Combine like terms: 1.685312368 + -1.416666667 = 0.268645701
y = 0.268645701

Simplifying
y = 0.268645701


Subproblem 2
y + 1.416666667 = -1.685312368

Simplifying
y + 1.416666667 = -1.685312368

Reorder the terms:
1.416666667 + y = -1.685312368

Solving
1.416666667 + y = -1.685312368

Solving for variable 'y'.

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

Add '-1.416666667' to each side of the equation.
1.416666667 + -1.416666667 + y = -1.685312368 + -1.416666667

Combine like terms: 1.416666667 + -1.416666667 = 0.000000000
0.000000000 + y = -1.685312368 + -1.416666667
y = -1.685312368 + -1.416666667

Combine like terms: -1.685312368 + -1.416666667 = -3.101979035
y = -3.101979035

Simplifying
y = -3.101979035


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.268645701, -3.101979035}

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