8x^2-54x+120=0

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Solution for 8x^2-54x+120=0 equation: 


Simplifying
8x2 + -54x + 120 = 0

Reorder the terms:
120 + -54x + 8x2 = 0

Solving
120 + -54x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(60 + -27x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(60 + -27x + 4x2)' equal to zero and attempt to solve:

Simplifying
60 + -27x + 4x2 = 0

Solving
60 + -27x + 4x2 = 0

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

Divide each side by '4'.
15 + -6.75x + x2 = 0

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -6.75x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + -6.75x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -6.75x + x2 = 0 + -15
-6.75x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
-6.75x + x2 = -15

The x term is -6.75x.  Take half its coefficient (-3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
-6.75x + 11.390625 + x2 = -15 + 11.390625

Reorder the terms:
11.390625 + -6.75x + x2 = -15 + 11.390625

Combine like terms: -15 + 11.390625 = -3.609375
11.390625 + -6.75x + x2 = -3.609375

Factor a perfect square on the left side:
(x + -3.375)(x + -3.375) = -3.609375

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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