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 = 4185
4225 + -130x + x2 = 4185

Factor a perfect square on the left side:
(x + -65)(x + -65) = 4185

Calculate the square root of the right side: 64.691575959

Break this problem into two subproblems by setting 
(x + -65) equal to 64.691575959 and -64.691575959.


Subproblem 1
x + -65 = 64.691575959

Simplifying
x + -65 = 64.691575959

Reorder the terms:
-65 + x = 64.691575959

Solving
-65 + x = 64.691575959

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 = 64.691575959 + 65

Combine like terms: -65 + 65 = 0
0 + x = 64.691575959 + 65
x = 64.691575959 + 65

Combine like terms: 64.691575959 + 65 = 129.691575959
x = 129.691575959

Simplifying
x = 129.691575959


Subproblem 2
x + -65 = -64.691575959

Simplifying
x + -65 = -64.691575959

Reorder the terms:
-65 + x = -64.691575959

Solving
-65 + x = -64.691575959

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 = -64.691575959 + 65

Combine like terms: -65 + 65 = 0
0 + x = -64.691575959 + 65
x = -64.691575959 + 65

Combine like terms: -64.691575959 + 65 = 0.308424041
x = 0.308424041

Simplifying
x = 0.308424041


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {129.691575959, 0.308424041}
Solution
x = {129.691575959, 0.308424041}

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