18x^2-60x+51=0

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Solution for 18x^2-60x+51=0 equation: 


Simplifying
18x2 + -60x + 51 = 0

Reorder the terms:
51 + -60x + 18x2 = 0

Solving
51 + -60x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(17 + -20x + 6x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(17 + -20x + 6x2)' equal to zero and attempt to solve:

Simplifying
17 + -20x + 6x2 = 0

Solving
17 + -20x + 6x2 = 0

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

Divide each side by '6'.
2.833333333 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '-2.833333333' to each side of the equation.
2.833333333 + -3.333333333x + -2.833333333 + x2 = 0 + -2.833333333

Reorder the terms:
2.833333333 + -2.833333333 + -3.333333333x + x2 = 0 + -2.833333333

Combine like terms: 2.833333333 + -2.833333333 = 0.000000000
0.000000000 + -3.333333333x + x2 = 0 + -2.833333333
-3.333333333x + x2 = 0 + -2.833333333

Combine like terms: 0 + -2.833333333 = -2.833333333
-3.333333333x + x2 = -2.833333333

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 = -2.833333333 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = -2.833333333 + 2.777777779

Combine like terms: -2.833333333 + 2.777777779 = -0.055555554
2.777777779 + -3.333333333x + x2 = -0.055555554

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = -0.055555554

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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