18x^2-81x+120=0

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Solution for 18x^2-81x+120=0 equation: 


Simplifying
18x2 + -81x + 120 = 0

Reorder the terms:
120 + -81x + 18x2 = 0

Solving
120 + -81x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(40 + -27x + 6x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(40 + -27x + 6x2)' equal to zero and attempt to solve:

Simplifying
40 + -27x + 6x2 = 0

Solving
40 + -27x + 6x2 = 0

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

Divide each side by '6'.
6.666666667 + -4.5x + x2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + -4.5x + -6.666666667 + x2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + -4.5x + x2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + -4.5x + x2 = 0 + -6.666666667
-4.5x + x2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
-4.5x + x2 = -6.666666667

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = -6.666666667 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = -6.666666667 + 5.0625

Combine like terms: -6.666666667 + 5.0625 = -1.604166667
5.0625 + -4.5x + x2 = -1.604166667

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = -1.604166667

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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