4y^2+3y-30=0

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Solution for 4y^2+3y-30=0 equation: 


Simplifying
4y2 + 3y + -30 = 0

Reorder the terms:
-30 + 3y + 4y2 = 0

Solving
-30 + 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'.
-7.5 + 0.75y + y2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 0.75y + 7.5 + y2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 0.75y + y2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 0.75y + y2 = 0 + 7.5
0.75y + y2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
0.75y + y2 = 7.5

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 = 7.5 + 0.140625

Reorder the terms:
0.140625 + 0.75y + y2 = 7.5 + 0.140625

Combine like terms: 7.5 + 0.140625 = 7.640625
0.140625 + 0.75y + y2 = 7.640625

Factor a perfect square on the left side:
(y + 0.375)(y + 0.375) = 7.640625

Calculate the square root of the right side: 2.764168048

Break this problem into two subproblems by setting 
(y + 0.375) equal to 2.764168048 and -2.764168048.


Subproblem 1
y + 0.375 = 2.764168048

Simplifying
y + 0.375 = 2.764168048

Reorder the terms:
0.375 + y = 2.764168048

Solving
0.375 + y = 2.764168048

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 = 2.764168048 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + y = 2.764168048 + -0.375
y = 2.764168048 + -0.375

Combine like terms: 2.764168048 + -0.375 = 2.389168048
y = 2.389168048

Simplifying
y = 2.389168048


Subproblem 2
y + 0.375 = -2.764168048

Simplifying
y + 0.375 = -2.764168048

Reorder the terms:
0.375 + y = -2.764168048

Solving
0.375 + y = -2.764168048

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 = -2.764168048 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + y = -2.764168048 + -0.375
y = -2.764168048 + -0.375

Combine like terms: -2.764168048 + -0.375 = -3.139168048
y = -3.139168048

Simplifying
y = -3.139168048


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.389168048, -3.139168048}

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