-6n^2+8n=5

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Solution for -6n^2+8n=5 equation: 


Simplifying
-6n2 + 8n = 5

Reorder the terms:
8n + -6n2 = 5

Solving
8n + -6n2 = 5

Solving for variable 'n'.

Reorder the terms:
-5 + 8n + -6n2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 8n + -6n2 = 0

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

Divide each side by '-6'.
0.8333333333 + -1.333333333n + n2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + -1.333333333n + -0.8333333333 + n2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + -1.333333333n + n2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + -1.333333333n + n2 = 0 + -0.8333333333
-1.333333333n + n2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
-1.333333333n + n2 = -0.8333333333

The n term is -1.333333333n.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333n + 0.4444444442 + n2 = -0.8333333333 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333n + n2 = -0.8333333333 + 0.4444444442

Combine like terms: -0.8333333333 + 0.4444444442 = -0.3888888891
0.4444444442 + -1.333333333n + n2 = -0.3888888891

Factor a perfect square on the left side:
(n + -0.6666666665)(n + -0.6666666665) = -0.3888888891

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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