15x^2+50x+120=0

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Solution for 15x^2+50x+120=0 equation: 


Simplifying
15x2 + 50x + 120 = 0

Reorder the terms:
120 + 50x + 15x2 = 0

Solving
120 + 50x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(24 + 10x + 3x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(24 + 10x + 3x2)' equal to zero and attempt to solve:

Simplifying
24 + 10x + 3x2 = 0

Solving
24 + 10x + 3x2 = 0

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

Divide each side by '3'.
8 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 3.333333333x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 3.333333333x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3.333333333x + x2 = 0 + -8
3.333333333x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
3.333333333x + x2 = -8

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 = -8 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = -8 + 2.777777779

Combine like terms: -8 + 2.777777779 = -5.222222221
2.777777779 + 3.333333333x + x2 = -5.222222221

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = -5.222222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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