6x^2-78x+320=0

Solution for 6x^2-78x+320=0 equation:

Simplifying
6x2 + -78x + 320 = 0

Reorder the terms:
320 + -78x + 6x2 = 0

Solving
320 + -78x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(160 + -39x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(160 + -39x + 3x2)' equal to zero and attempt to solve:

Simplifying
160 + -39x + 3x2 = 0

Solving
160 + -39x + 3x2 = 0

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

Divide each side by '3'.
53.33333333 + -13x + x2 = 0

Move the constant term to the right:

Add '-53.33333333' to each side of the equation.
53.33333333 + -13x + -53.33333333 + x2 = 0 + -53.33333333

Reorder the terms:
53.33333333 + -53.33333333 + -13x + x2 = 0 + -53.33333333

Combine like terms: 53.33333333 + -53.33333333 = 0.00000000
0.00000000 + -13x + x2 = 0 + -53.33333333
-13x + x2 = 0 + -53.33333333

Combine like terms: 0 + -53.33333333 = -53.33333333
-13x + x2 = -53.33333333

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -53.33333333 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -53.33333333 + 42.25

Combine like terms: -53.33333333 + 42.25 = -11.08333333
42.25 + -13x + x2 = -11.08333333

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = -11.08333333

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.