3a^2-51a+21=0

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Solution for 3a^2-51a+21=0 equation: 


Simplifying
3a2 + -51a + 21 = 0

Reorder the terms:
21 + -51a + 3a2 = 0

Solving
21 + -51a + 3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + -17a + a2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + -17a + a2)' equal to zero and attempt to solve:

Simplifying
7 + -17a + a2 = 0

Solving
7 + -17a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -17a + -7 + a2 = 0 + -7

Reorder the terms:
7 + -7 + -17a + a2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -17a + a2 = 0 + -7
-17a + a2 = 0 + -7

Combine like terms: 0 + -7 = -7
-17a + a2 = -7

The a term is -17a.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17a + 72.25 + a2 = -7 + 72.25

Reorder the terms:
72.25 + -17a + a2 = -7 + 72.25

Combine like terms: -7 + 72.25 = 65.25
72.25 + -17a + a2 = 65.25

Factor a perfect square on the left side:
(a + -8.5)(a + -8.5) = 65.25

Calculate the square root of the right side: 8.077747211

Break this problem into two subproblems by setting 
(a + -8.5) equal to 8.077747211 and -8.077747211.


Subproblem 1
a + -8.5 = 8.077747211

Simplifying
a + -8.5 = 8.077747211

Reorder the terms:
-8.5 + a = 8.077747211

Solving
-8.5 + a = 8.077747211

Solving for variable 'a'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + a = 8.077747211 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + a = 8.077747211 + 8.5
a = 8.077747211 + 8.5

Combine like terms: 8.077747211 + 8.5 = 16.577747211
a = 16.577747211

Simplifying
a = 16.577747211


Subproblem 2
a + -8.5 = -8.077747211

Simplifying
a + -8.5 = -8.077747211

Reorder the terms:
-8.5 + a = -8.077747211

Solving
-8.5 + a = -8.077747211

Solving for variable 'a'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + a = -8.077747211 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + a = -8.077747211 + 8.5
a = -8.077747211 + 8.5

Combine like terms: -8.077747211 + 8.5 = 0.422252789
a = 0.422252789

Simplifying
a = 0.422252789


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {16.577747211, 0.422252789}
Solution
a = {16.577747211, 0.422252789}

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