9x^2+24x+45=0

Solution for 9x^2+24x+45=0 equation:

Simplifying
9x2 + 24x + 45 = 0

Reorder the terms:
45 + 24x + 9x2 = 0

Solving
45 + 24x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + 8x + 3x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(15 + 8x + 3x2)' equal to zero and attempt to solve:

Simplifying
15 + 8x + 3x2 = 0

Solving
15 + 8x + 3x2 = 0

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

Divide each side by '3'.
5 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 2.666666667x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 2.666666667x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2.666666667x + x2 = 0 + -5
2.666666667x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
2.666666667x + x2 = -5

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = -5 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = -5 + 1.777777780

Combine like terms: -5 + 1.777777780 = -3.22222222
1.777777780 + 2.666666667x + x2 = -3.22222222

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = -3.22222222

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.