3x^2-10x-120=0

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Solution for 3x^2-10x-120=0 equation: 


Simplifying
3x2 + -10x + -120 = 0

Reorder the terms:
-120 + -10x + 3x2 = 0

Solving
-120 + -10x + 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 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -3.333333333x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -3.333333333x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -3.333333333x + x2 = 0 + 40
-3.333333333x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-3.333333333x + x2 = 40

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 40 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 40 + 2.777777779

Combine like terms: 40 + 2.777777779 = 42.777777779
2.777777779 + -3.333333333x + x2 = 42.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 42.777777779

Calculate the square root of the right side: 6.54047229

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 6.54047229 and -6.54047229.


Subproblem 1
x + -1.666666667 = 6.54047229

Simplifying
x + -1.666666667 = 6.54047229

Reorder the terms:
-1.666666667 + x = 6.54047229

Solving
-1.666666667 + x = 6.54047229

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 6.54047229 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 6.54047229 + 1.666666667
x = 6.54047229 + 1.666666667

Combine like terms: 6.54047229 + 1.666666667 = 8.207138957
x = 8.207138957

Simplifying
x = 8.207138957


Subproblem 2
x + -1.666666667 = -6.54047229

Simplifying
x + -1.666666667 = -6.54047229

Reorder the terms:
-1.666666667 + x = -6.54047229

Solving
-1.666666667 + x = -6.54047229

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -6.54047229 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -6.54047229 + 1.666666667
x = -6.54047229 + 1.666666667

Combine like terms: -6.54047229 + 1.666666667 = -4.873805623
x = -4.873805623

Simplifying
x = -4.873805623


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.207138957, -4.873805623}

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