4y^2-3y-63=0

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Solution for 4y^2-3y-63=0 equation: 


Simplifying
4y2 + -3y + -63 = 0

Reorder the terms:
-63 + -3y + 4y2 = 0

Solving
-63 + -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'.
-15.75 + -0.75y + y2 = 0

Move the constant term to the right:

Add '15.75' to each side of the equation.
-15.75 + -0.75y + 15.75 + y2 = 0 + 15.75

Reorder the terms:
-15.75 + 15.75 + -0.75y + y2 = 0 + 15.75

Combine like terms: -15.75 + 15.75 = 0.00
0.00 + -0.75y + y2 = 0 + 15.75
-0.75y + y2 = 0 + 15.75

Combine like terms: 0 + 15.75 = 15.75
-0.75y + y2 = 15.75

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 = 15.75 + 0.140625

Reorder the terms:
0.140625 + -0.75y + y2 = 15.75 + 0.140625

Combine like terms: 15.75 + 0.140625 = 15.890625
0.140625 + -0.75y + y2 = 15.890625

Factor a perfect square on the left side:
(y + -0.375)(y + -0.375) = 15.890625

Calculate the square root of the right side: 3.98630468

Break this problem into two subproblems by setting 
(y + -0.375) equal to 3.98630468 and -3.98630468.


Subproblem 1
y + -0.375 = 3.98630468

Simplifying
y + -0.375 = 3.98630468

Reorder the terms:
-0.375 + y = 3.98630468

Solving
-0.375 + y = 3.98630468

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 = 3.98630468 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + y = 3.98630468 + 0.375
y = 3.98630468 + 0.375

Combine like terms: 3.98630468 + 0.375 = 4.36130468
y = 4.36130468

Simplifying
y = 4.36130468


Subproblem 2
y + -0.375 = -3.98630468

Simplifying
y + -0.375 = -3.98630468

Reorder the terms:
-0.375 + y = -3.98630468

Solving
-0.375 + y = -3.98630468

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 = -3.98630468 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + y = -3.98630468 + 0.375
y = -3.98630468 + 0.375

Combine like terms: -3.98630468 + 0.375 = -3.61130468
y = -3.61130468

Simplifying
y = -3.61130468


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.36130468, -3.61130468}

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