6x^2-12x+20=5

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Solution for 6x^2-12x+20=5 equation: 


Simplifying
6x2 + -12x + 20 = 5

Reorder the terms:
20 + -12x + 6x2 = 5

Solving
20 + -12x + 6x2 = 5

Solving for variable 'x'.

Reorder the terms:
20 + -5 + -12x + 6x2 = 5 + -5

Combine like terms: 20 + -5 = 15
15 + -12x + 6x2 = 5 + -5

Combine like terms: 5 + -5 = 0
15 + -12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -4x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5 + -4x + 2x2)' equal to zero and attempt to solve:

Simplifying
5 + -4x + 2x2 = 0

Solving
5 + -4x + 2x2 = 0

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

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

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -2x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -2x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -2x + x2 = 0 + -2.5
-2x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-2x + x2 = -2.5

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -2.5 + 1

Reorder the terms:
1 + -2x + x2 = -2.5 + 1

Combine like terms: -2.5 + 1 = -1.5
1 + -2x + x2 = -1.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = -1.5

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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