3x^2-18x=6x+5

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Solution for 3x^2-18x=6x+5 equation: 


Simplifying
3x2 + -18x = 6x + 5

Reorder the terms:
-18x + 3x2 = 6x + 5

Reorder the terms:
-18x + 3x2 = 5 + 6x

Solving
-18x + 3x2 = 5 + 6x

Solving for variable 'x'.

Reorder the terms:
-5 + -18x + -6x + 3x2 = 5 + 6x + -5 + -6x

Combine like terms: -18x + -6x = -24x
-5 + -24x + 3x2 = 5 + 6x + -5 + -6x

Reorder the terms:
-5 + -24x + 3x2 = 5 + -5 + 6x + -6x

Combine like terms: 5 + -5 = 0
-5 + -24x + 3x2 = 0 + 6x + -6x
-5 + -24x + 3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-5 + -24x + 3x2 = 0

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

Divide each side by '3'.
-1.666666667 + -8x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -8x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -8x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -8x + x2 = 0 + 1.666666667
-8x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-8x + x2 = 1.666666667

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 1.666666667 + 16

Reorder the terms:
16 + -8x + x2 = 1.666666667 + 16

Combine like terms: 1.666666667 + 16 = 17.666666667
16 + -8x + x2 = 17.666666667

Factor a perfect square on the left side:
(x + -4)(x + -4) = 17.666666667

Calculate the square root of the right side: 4.203173404

Break this problem into two subproblems by setting 
(x + -4) equal to 4.203173404 and -4.203173404.


Subproblem 1
x + -4 = 4.203173404

Simplifying
x + -4 = 4.203173404

Reorder the terms:
-4 + x = 4.203173404

Solving
-4 + x = 4.203173404

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 4.203173404 + 4

Combine like terms: -4 + 4 = 0
0 + x = 4.203173404 + 4
x = 4.203173404 + 4

Combine like terms: 4.203173404 + 4 = 8.203173404
x = 8.203173404

Simplifying
x = 8.203173404


Subproblem 2
x + -4 = -4.203173404

Simplifying
x + -4 = -4.203173404

Reorder the terms:
-4 + x = -4.203173404

Solving
-4 + x = -4.203173404

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -4.203173404 + 4

Combine like terms: -4 + 4 = 0
0 + x = -4.203173404 + 4
x = -4.203173404 + 4

Combine like terms: -4.203173404 + 4 = -0.203173404
x = -0.203173404

Simplifying
x = -0.203173404


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.203173404, -0.203173404}

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