9=a(a-83)

Solution for 9=a(a-83) equation:

Simplifying
9 = a(a + -83)

Reorder the terms:
9 = a(-83 + a)
9 = (-83 * a + a * a)
9 = (-83a + a2)

Solving
9 = -83a + a2

Solving for variable 'a'.

Reorder the terms:
9 + 83a + -1a2 = -83a + 83a + a2 + -1a2

Combine like terms: -83a + 83a = 0
9 + 83a + -1a2 = 0 + a2 + -1a2
9 + 83a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
9 + 83a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-9 + -83a + a2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -83a + 9 + a2 = 0 + 9

Reorder the terms:
-9 + 9 + -83a + a2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -83a + a2 = 0 + 9
-83a + a2 = 0 + 9

Combine like terms: 0 + 9 = 9
-83a + a2 = 9

The a term is -83a.  Take half its coefficient (-41.5).
Square it (1722.25) and add it to both sides.

Add '1722.25' to each side of the equation.
-83a + 1722.25 + a2 = 9 + 1722.25

Reorder the terms:
1722.25 + -83a + a2 = 9 + 1722.25

Combine like terms: 9 + 1722.25 = 1731.25
1722.25 + -83a + a2 = 1731.25

Factor a perfect square on the left side:
(a + -41.5)(a + -41.5) = 1731.25

Calculate the square root of the right side: 41.608292443

Break this problem into two subproblems by setting 
(a + -41.5) equal to 41.608292443 and -41.608292443.

Subproblem 1
a + -41.5 = 41.608292443

Simplifying
a + -41.5 = 41.608292443

Reorder the terms:
-41.5 + a = 41.608292443

Solving
-41.5 + a = 41.608292443

Solving for variable 'a'.

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

Add '41.5' to each side of the equation.
-41.5 + 41.5 + a = 41.608292443 + 41.5

Combine like terms: -41.5 + 41.5 = 0.0
0.0 + a = 41.608292443 + 41.5
a = 41.608292443 + 41.5

Combine like terms: 41.608292443 + 41.5 = 83.108292443
a = 83.108292443

Simplifying
a = 83.108292443

Subproblem 2
a + -41.5 = -41.608292443

Simplifying
a + -41.5 = -41.608292443

Reorder the terms:
-41.5 + a = -41.608292443

Solving
-41.5 + a = -41.608292443

Solving for variable 'a'.

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

Add '41.5' to each side of the equation.
-41.5 + 41.5 + a = -41.608292443 + 41.5

Combine like terms: -41.5 + 41.5 = 0.0
0.0 + a = -41.608292443 + 41.5
a = -41.608292443 + 41.5

Combine like terms: -41.608292443 + 41.5 = -0.108292443
a = -0.108292443

Simplifying
a = -0.108292443

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {83.108292443, -0.108292443}