21a^2-51a+36=0

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Solution for 21a^2-51a+36=0 equation: 


Simplifying
21a2 + -51a + 36 = 0

Reorder the terms:
36 + -51a + 21a2 = 0

Solving
36 + -51a + 21a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -17a + 7a2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(12 + -17a + 7a2)' equal to zero and attempt to solve:

Simplifying
12 + -17a + 7a2 = 0

Solving
12 + -17a + 7a2 = 0

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

Divide each side by '7'.
1.714285714 + -2.428571429a + a2 = 0

Move the constant term to the right:

Add '-1.714285714' to each side of the equation.
1.714285714 + -2.428571429a + -1.714285714 + a2 = 0 + -1.714285714

Reorder the terms:
1.714285714 + -1.714285714 + -2.428571429a + a2 = 0 + -1.714285714

Combine like terms: 1.714285714 + -1.714285714 = 0.000000000
0.000000000 + -2.428571429a + a2 = 0 + -1.714285714
-2.428571429a + a2 = 0 + -1.714285714

Combine like terms: 0 + -1.714285714 = -1.714285714
-2.428571429a + a2 = -1.714285714

The a term is -2.428571429a.  Take half its coefficient (-1.214285715).
Square it (1.474489798) and add it to both sides.

Add '1.474489798' to each side of the equation.
-2.428571429a + 1.474489798 + a2 = -1.714285714 + 1.474489798

Reorder the terms:
1.474489798 + -2.428571429a + a2 = -1.714285714 + 1.474489798

Combine like terms: -1.714285714 + 1.474489798 = -0.239795916
1.474489798 + -2.428571429a + a2 = -0.239795916

Factor a perfect square on the left side:
(a + -1.214285715)(a + -1.214285715) = -0.239795916

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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