4y^2-3y-15=0

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Solution for 4y^2-3y-15=0 equation:


Simplifying
4y2 + -3y + -15 = 0

Reorder the terms:
-15 + -3y + 4y2 = 0

Solving
-15 + -3y + 4y2 = 0

Solving for variable 'y'.

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

Divide each side by '4'.
-3.75 + -0.75y + y2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -0.75y + 3.75 + y2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -0.75y + y2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -0.75y + y2 = 0 + 3.75
-0.75y + y2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-0.75y + y2 = 3.75

The y term is -0.75y.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75y + 0.140625 + y2 = 3.75 + 0.140625

Reorder the terms:
0.140625 + -0.75y + y2 = 3.75 + 0.140625

Combine like terms: 3.75 + 0.140625 = 3.890625
0.140625 + -0.75y + y2 = 3.890625

Factor a perfect square on the left side:
(y + -0.375)(y + -0.375) = 3.890625

Calculate the square root of the right side: 1.97246673

Break this problem into two subproblems by setting 
(y + -0.375) equal to 1.97246673 and -1.97246673.

Subproblem 1

y + -0.375 = 1.97246673 Simplifying y + -0.375 = 1.97246673 Reorder the terms: -0.375 + y = 1.97246673 Solving -0.375 + y = 1.97246673 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + y = 1.97246673 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + y = 1.97246673 + 0.375 y = 1.97246673 + 0.375 Combine like terms: 1.97246673 + 0.375 = 2.34746673 y = 2.34746673 Simplifying y = 2.34746673

Subproblem 2

y + -0.375 = -1.97246673 Simplifying y + -0.375 = -1.97246673 Reorder the terms: -0.375 + y = -1.97246673 Solving -0.375 + y = -1.97246673 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + y = -1.97246673 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + y = -1.97246673 + 0.375 y = -1.97246673 + 0.375 Combine like terms: -1.97246673 + 0.375 = -1.59746673 y = -1.59746673 Simplifying y = -1.59746673

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.34746673, -1.59746673}

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