3y^2-13y-6=

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Solution for 3y^2-13y-6= equation:


Simplifying
3y2 + -13y + -6 = 0

Reorder the terms:
-6 + -13y + 3y2 = 0

Solving
-6 + -13y + 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'.
-2 + -4.333333333y + y2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -4.333333333y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + -4.333333333y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -4.333333333y + y2 = 0 + 2
-4.333333333y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
-4.333333333y + y2 = 2

The y term is -4.333333333y.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333y + 4.694444446 + y2 = 2 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333y + y2 = 2 + 4.694444446

Combine like terms: 2 + 4.694444446 = 6.694444446
4.694444446 + -4.333333333y + y2 = 6.694444446

Factor a perfect square on the left side:
(y + -2.166666667)(y + -2.166666667) = 6.694444446

Calculate the square root of the right side: 2.58736245

Break this problem into two subproblems by setting 
(y + -2.166666667) equal to 2.58736245 and -2.58736245.

Subproblem 1

y + -2.166666667 = 2.58736245 Simplifying y + -2.166666667 = 2.58736245 Reorder the terms: -2.166666667 + y = 2.58736245 Solving -2.166666667 + y = 2.58736245 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + y = 2.58736245 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + y = 2.58736245 + 2.166666667 y = 2.58736245 + 2.166666667 Combine like terms: 2.58736245 + 2.166666667 = 4.754029117 y = 4.754029117 Simplifying y = 4.754029117

Subproblem 2

y + -2.166666667 = -2.58736245 Simplifying y + -2.166666667 = -2.58736245 Reorder the terms: -2.166666667 + y = -2.58736245 Solving -2.166666667 + y = -2.58736245 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + y = -2.58736245 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + y = -2.58736245 + 2.166666667 y = -2.58736245 + 2.166666667 Combine like terms: -2.58736245 + 2.166666667 = -0.420695783 y = -0.420695783 Simplifying y = -0.420695783

Solution

The solution to the problem is based on the solutions from the subproblems. y = {4.754029117, -0.420695783}

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