3x^2+32.4x-120=0

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Solution for 3x^2+32.4x-120=0 equation: 


Simplifying
3x2 + 32.4x + -120 = 0

Reorder the terms:
-120 + 32.4x + 3x2 = 0

Solving
-120 + 32.4x + 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'.
-40 + 10.8x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 10.8x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 10.8x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 10.8x + x2 = 0 + 40
10.8x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
10.8x + x2 = 40

The x term is 10.8x.  Take half its coefficient (5.4).
Square it (29.16) and add it to both sides.

Add '29.16' to each side of the equation.
10.8x + 29.16 + x2 = 40 + 29.16

Reorder the terms:
29.16 + 10.8x + x2 = 40 + 29.16

Combine like terms: 40 + 29.16 = 69.16
29.16 + 10.8x + x2 = 69.16

Factor a perfect square on the left side:
(x + 5.4)(x + 5.4) = 69.16

Calculate the square root of the right side: 8.316249155

Break this problem into two subproblems by setting 
(x + 5.4) equal to 8.316249155 and -8.316249155.


Subproblem 1
x + 5.4 = 8.316249155

Simplifying
x + 5.4 = 8.316249155

Reorder the terms:
5.4 + x = 8.316249155

Solving
5.4 + x = 8.316249155

Solving for variable 'x'.

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

Add '-5.4' to each side of the equation.
5.4 + -5.4 + x = 8.316249155 + -5.4

Combine like terms: 5.4 + -5.4 = 0.0
0.0 + x = 8.316249155 + -5.4
x = 8.316249155 + -5.4

Combine like terms: 8.316249155 + -5.4 = 2.916249155
x = 2.916249155

Simplifying
x = 2.916249155


Subproblem 2
x + 5.4 = -8.316249155

Simplifying
x + 5.4 = -8.316249155

Reorder the terms:
5.4 + x = -8.316249155

Solving
5.4 + x = -8.316249155

Solving for variable 'x'.

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

Add '-5.4' to each side of the equation.
5.4 + -5.4 + x = -8.316249155 + -5.4

Combine like terms: 5.4 + -5.4 = 0.0
0.0 + x = -8.316249155 + -5.4
x = -8.316249155 + -5.4

Combine like terms: -8.316249155 + -5.4 = -13.716249155
x = -13.716249155

Simplifying
x = -13.716249155


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.916249155, -13.716249155}

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