-4y^2+18y-3=0

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Solution for -4y^2+18y-3=0 equation: 


Simplifying
-4y2 + 18y + -3 = 0

Reorder the terms:
-3 + 18y + -4y2 = 0

Solving
-3 + 18y + -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'.
0.75 + -4.5y + y2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -4.5y + -0.75 + y2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -4.5y + y2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -4.5y + y2 = 0 + -0.75
-4.5y + y2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-4.5y + y2 = -0.75

The y term is -4.5y.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5y + 5.0625 + y2 = -0.75 + 5.0625

Reorder the terms:
5.0625 + -4.5y + y2 = -0.75 + 5.0625

Combine like terms: -0.75 + 5.0625 = 4.3125
5.0625 + -4.5y + y2 = 4.3125

Factor a perfect square on the left side:
(y + -2.25)(y + -2.25) = 4.3125

Calculate the square root of the right side: 2.076655966

Break this problem into two subproblems by setting 
(y + -2.25) equal to 2.076655966 and -2.076655966.


Subproblem 1
y + -2.25 = 2.076655966

Simplifying
y + -2.25 = 2.076655966

Reorder the terms:
-2.25 + y = 2.076655966

Solving
-2.25 + y = 2.076655966

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '2.25' to each side of the equation.
-2.25 + 2.25 + y = 2.076655966 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + y = 2.076655966 + 2.25
y = 2.076655966 + 2.25

Combine like terms: 2.076655966 + 2.25 = 4.326655966
y = 4.326655966

Simplifying
y = 4.326655966


Subproblem 2
y + -2.25 = -2.076655966

Simplifying
y + -2.25 = -2.076655966

Reorder the terms:
-2.25 + y = -2.076655966

Solving
-2.25 + y = -2.076655966

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '2.25' to each side of the equation.
-2.25 + 2.25 + y = -2.076655966 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + y = -2.076655966 + 2.25
y = -2.076655966 + 2.25

Combine like terms: -2.076655966 + 2.25 = 0.173344034
y = 0.173344034

Simplifying
y = 0.173344034


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.326655966, 0.173344034}

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