-6v^2+17v-8=0

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Solution for -6v^2+17v-8=0 equation: 


Simplifying
-6v2 + 17v + -8 = 0

Reorder the terms:
-8 + 17v + -6v2 = 0

Solving
-8 + 17v + -6v2 = 0

Solving for variable 'v'.

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

Divide each side by '-6'.
1.333333333 + -2.833333333v + v2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -2.833333333v + -1.333333333 + v2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -2.833333333v + v2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -2.833333333v + v2 = 0 + -1.333333333
-2.833333333v + v2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-2.833333333v + v2 = -1.333333333

The v term is -2.833333333v.  Take half its coefficient (-1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
-2.833333333v + 2.006944445 + v2 = -1.333333333 + 2.006944445

Reorder the terms:
2.006944445 + -2.833333333v + v2 = -1.333333333 + 2.006944445

Combine like terms: -1.333333333 + 2.006944445 = 0.673611112
2.006944445 + -2.833333333v + v2 = 0.673611112

Factor a perfect square on the left side:
(v + -1.416666667)(v + -1.416666667) = 0.673611112

Calculate the square root of the right side: 0.820738151

Break this problem into two subproblems by setting 
(v + -1.416666667) equal to 0.820738151 and -0.820738151.


Subproblem 1
v + -1.416666667 = 0.820738151

Simplifying
v + -1.416666667 = 0.820738151

Reorder the terms:
-1.416666667 + v = 0.820738151

Solving
-1.416666667 + v = 0.820738151

Solving for variable 'v'.

Move all terms containing v to the left, all other terms to the right.

Add '1.416666667' to each side of the equation.
-1.416666667 + 1.416666667 + v = 0.820738151 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + v = 0.820738151 + 1.416666667
v = 0.820738151 + 1.416666667

Combine like terms: 0.820738151 + 1.416666667 = 2.237404818
v = 2.237404818

Simplifying
v = 2.237404818


Subproblem 2
v + -1.416666667 = -0.820738151

Simplifying
v + -1.416666667 = -0.820738151

Reorder the terms:
-1.416666667 + v = -0.820738151

Solving
-1.416666667 + v = -0.820738151

Solving for variable 'v'.

Move all terms containing v to the left, all other terms to the right.

Add '1.416666667' to each side of the equation.
-1.416666667 + 1.416666667 + v = -0.820738151 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + v = -0.820738151 + 1.416666667
v = -0.820738151 + 1.416666667

Combine like terms: -0.820738151 + 1.416666667 = 0.595928516
v = 0.595928516

Simplifying
v = 0.595928516


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {2.237404818, 0.595928516}

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