3x^2+390x-120=0

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Solution for 3x^2+390x-120=0 equation: 


Simplifying
3x2 + 390x + -120 = 0

Reorder the terms:
-120 + 390x + 3x2 = 0

Solving
-120 + 390x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-40 + 130x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-40 + 130x + x2)' equal to zero and attempt to solve:

Simplifying
-40 + 130x + x2 = 0

Solving
-40 + 130x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 130x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 130x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 130x + x2 = 0 + 40
130x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
130x + x2 = 40

The x term is 130x.  Take half its coefficient (65).
Square it (4225) and add it to both sides.

Add '4225' to each side of the equation.
130x + 4225 + x2 = 40 + 4225

Reorder the terms:
4225 + 130x + x2 = 40 + 4225

Combine like terms: 40 + 4225 = 4265
4225 + 130x + x2 = 4265

Factor a perfect square on the left side:
(x + 65)(x + 65) = 4265

Calculate the square root of the right side: 65.306967469

Break this problem into two subproblems by setting 
(x + 65) equal to 65.306967469 and -65.306967469.


Subproblem 1
x + 65 = 65.306967469

Simplifying
x + 65 = 65.306967469

Reorder the terms:
65 + x = 65.306967469

Solving
65 + x = 65.306967469

Solving for variable 'x'.

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

Add '-65' to each side of the equation.
65 + -65 + x = 65.306967469 + -65

Combine like terms: 65 + -65 = 0
0 + x = 65.306967469 + -65
x = 65.306967469 + -65

Combine like terms: 65.306967469 + -65 = 0.306967469
x = 0.306967469

Simplifying
x = 0.306967469


Subproblem 2
x + 65 = -65.306967469

Simplifying
x + 65 = -65.306967469

Reorder the terms:
65 + x = -65.306967469

Solving
65 + x = -65.306967469

Solving for variable 'x'.

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

Add '-65' to each side of the equation.
65 + -65 + x = -65.306967469 + -65

Combine like terms: 65 + -65 = 0
0 + x = -65.306967469 + -65
x = -65.306967469 + -65

Combine like terms: -65.306967469 + -65 = -130.306967469
x = -130.306967469

Simplifying
x = -130.306967469


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.306967469, -130.306967469}
Solution
x = {0.306967469, -130.306967469}

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