30x^2+15x+20=0

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Solution for 30x^2+15x+20=0 equation: 


Simplifying
30x2 + 15x + 20 = 0

Reorder the terms:
20 + 15x + 30x2 = 0

Solving
20 + 15x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(4 + 3x + 6x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(4 + 3x + 6x2)' equal to zero and attempt to solve:

Simplifying
4 + 3x + 6x2 = 0

Solving
4 + 3x + 6x2 = 0

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

Divide each side by '6'.
0.6666666667 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 0.5x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 0.5x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 0.5x + x2 = 0 + -0.6666666667
0.5x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
0.5x + x2 = -0.6666666667

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = -0.6666666667 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = -0.6666666667 + 0.0625

Combine like terms: -0.6666666667 + 0.0625 = -0.6041666667
0.0625 + 0.5x + x2 = -0.6041666667

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = -0.6041666667

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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