(6x^2)-15x+39=0

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Solution for (6x^2)-15x+39=0 equation: 


Simplifying
(6x2) + -15x + 39 = 0

Reorder the terms:
39 + -15x + (6x2) = 0

Solving
39 + -15x + (6x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(13 + -5x + (2x2)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(13 + -5x + (2x2))' equal to zero and attempt to solve:

Simplifying
13 + -5x + (2x2) = 0

Solving
13 + -5x + (2x2) = 0

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

Divide each side by '2'.
6.5 + -2.5x + x2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + -2.5x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + -2.5x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + -2.5x + x2 = 0 + -6.5
-2.5x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
-2.5x + x2 = -6.5

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = -6.5 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = -6.5 + 1.5625

Combine like terms: -6.5 + 1.5625 = -4.9375
1.5625 + -2.5x + x2 = -4.9375

Factor a perfect square on the left side:
((x) + -1.25)((x) + -1.25) = -4.9375

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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