18x-3x^2+5=0

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Solution for 18x-3x^2+5=0 equation: 


Simplifying
18x + -3x2 + 5 = 0

Reorder the terms:
5 + 18x + -3x2 = 0

Solving
5 + 18x + -3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-1.666666667 + -6x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -6x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -6x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -6x + x2 = 0 + 1.666666667
-6x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-6x + x2 = 1.666666667

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 1.666666667 + 9

Reorder the terms:
9 + -6x + x2 = 1.666666667 + 9

Combine like terms: 1.666666667 + 9 = 10.666666667
9 + -6x + x2 = 10.666666667

Factor a perfect square on the left side:
(x + -3)(x + -3) = 10.666666667

Calculate the square root of the right side: 3.265986324

Break this problem into two subproblems by setting 
(x + -3) equal to 3.265986324 and -3.265986324.


Subproblem 1
x + -3 = 3.265986324

Simplifying
x + -3 = 3.265986324

Reorder the terms:
-3 + x = 3.265986324

Solving
-3 + x = 3.265986324

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 3.265986324 + 3

Combine like terms: -3 + 3 = 0
0 + x = 3.265986324 + 3
x = 3.265986324 + 3

Combine like terms: 3.265986324 + 3 = 6.265986324
x = 6.265986324

Simplifying
x = 6.265986324


Subproblem 2
x + -3 = -3.265986324

Simplifying
x + -3 = -3.265986324

Reorder the terms:
-3 + x = -3.265986324

Solving
-3 + x = -3.265986324

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -3.265986324 + 3

Combine like terms: -3 + 3 = 0
0 + x = -3.265986324 + 3
x = -3.265986324 + 3

Combine like terms: -3.265986324 + 3 = -0.265986324
x = -0.265986324

Simplifying
x = -0.265986324


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.265986324, -0.265986324}

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