16a^2-24a-39=0

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Solution for 16a^2-24a-39=0 equation: 


Simplifying
16a2 + -24a + -39 = 0

Reorder the terms:
-39 + -24a + 16a2 = 0

Solving
-39 + -24a + 16a2 = 0

Solving for variable 'a'.

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

Divide each side by '16'.
-2.4375 + -1.5a + a2 = 0

Move the constant term to the right:

Add '2.4375' to each side of the equation.
-2.4375 + -1.5a + 2.4375 + a2 = 0 + 2.4375

Reorder the terms:
-2.4375 + 2.4375 + -1.5a + a2 = 0 + 2.4375

Combine like terms: -2.4375 + 2.4375 = 0.0000
0.0000 + -1.5a + a2 = 0 + 2.4375
-1.5a + a2 = 0 + 2.4375

Combine like terms: 0 + 2.4375 = 2.4375
-1.5a + a2 = 2.4375

The a term is -1.5a.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5a + 0.5625 + a2 = 2.4375 + 0.5625

Reorder the terms:
0.5625 + -1.5a + a2 = 2.4375 + 0.5625

Combine like terms: 2.4375 + 0.5625 = 3
0.5625 + -1.5a + a2 = 3

Factor a perfect square on the left side:
(a + -0.75)(a + -0.75) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(a + -0.75) equal to 1.732050808 and -1.732050808.


Subproblem 1
a + -0.75 = 1.732050808

Simplifying
a + -0.75 = 1.732050808

Reorder the terms:
-0.75 + a = 1.732050808

Solving
-0.75 + a = 1.732050808

Solving for variable 'a'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + a = 1.732050808 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + a = 1.732050808 + 0.75
a = 1.732050808 + 0.75

Combine like terms: 1.732050808 + 0.75 = 2.482050808
a = 2.482050808

Simplifying
a = 2.482050808


Subproblem 2
a + -0.75 = -1.732050808

Simplifying
a + -0.75 = -1.732050808

Reorder the terms:
-0.75 + a = -1.732050808

Solving
-0.75 + a = -1.732050808

Solving for variable 'a'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + a = -1.732050808 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + a = -1.732050808 + 0.75
a = -1.732050808 + 0.75

Combine like terms: -1.732050808 + 0.75 = -0.982050808
a = -0.982050808

Simplifying
a = -0.982050808


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.482050808, -0.982050808}

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