6y^2-45y=8

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Solution for 6y^2-45y=8 equation:


Simplifying
6y2 + -45y = 8

Reorder the terms:
-45y + 6y2 = 8

Solving
-45y + 6y2 = 8

Solving for variable 'y'.

Reorder the terms:
-8 + -45y + 6y2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -45y + 6y2 = 0

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

Divide each side by '6'.
-1.333333333 + -7.5y + y2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -7.5y + 1.333333333 + y2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -7.5y + y2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -7.5y + y2 = 0 + 1.333333333
-7.5y + y2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-7.5y + y2 = 1.333333333

The y term is -7.5y.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5y + 14.0625 + y2 = 1.333333333 + 14.0625

Reorder the terms:
14.0625 + -7.5y + y2 = 1.333333333 + 14.0625

Combine like terms: 1.333333333 + 14.0625 = 15.395833333
14.0625 + -7.5y + y2 = 15.395833333

Factor a perfect square on the left side:
(y + -3.75)(y + -3.75) = 15.395833333

Calculate the square root of the right side: 3.923752456

Break this problem into two subproblems by setting 
(y + -3.75) equal to 3.923752456 and -3.923752456.

Subproblem 1

y + -3.75 = 3.923752456 Simplifying y + -3.75 = 3.923752456 Reorder the terms: -3.75 + y = 3.923752456 Solving -3.75 + y = 3.923752456 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + y = 3.923752456 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + y = 3.923752456 + 3.75 y = 3.923752456 + 3.75 Combine like terms: 3.923752456 + 3.75 = 7.673752456 y = 7.673752456 Simplifying y = 7.673752456

Subproblem 2

y + -3.75 = -3.923752456 Simplifying y + -3.75 = -3.923752456 Reorder the terms: -3.75 + y = -3.923752456 Solving -3.75 + y = -3.923752456 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + y = -3.923752456 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + y = -3.923752456 + 3.75 y = -3.923752456 + 3.75 Combine like terms: -3.923752456 + 3.75 = -0.173752456 y = -0.173752456 Simplifying y = -0.173752456

Solution

The solution to the problem is based on the solutions from the subproblems. y = {7.673752456, -0.173752456}

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