-8a^2+a+15=0

Solution for -8a^2+a+15=0 equation:

Simplifying
-8a2 + a + 15 = 0

Reorder the terms:
15 + a + -8a2 = 0

Solving
15 + a + -8a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-1.875 + -0.125a + a2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + -0.125a + 1.875 + a2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + -0.125a + a2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + -0.125a + a2 = 0 + 1.875
-0.125a + a2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
-0.125a + a2 = 1.875

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.125a + 0.25 + a2 = 1.875 + 0.25

Reorder the terms:
0.25 + -0.125a + a2 = 1.875 + 0.25

Combine like terms: 1.875 + 0.25 = 2.125
0.25 + -0.125a + a2 = 2.125

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 2.125

Calculate the square root of the right side: 1.457737974

Break this problem into two subproblems by setting 
(a + 0.5) equal to 1.457737974 and -1.457737974.

Subproblem 1
a + 0.5 = 1.457737974

Simplifying
a + 0.5 = 1.457737974

Reorder the terms:
0.5 + a = 1.457737974

Solving
0.5 + a = 1.457737974

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = 1.457737974 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 1.457737974 + -0.5
a = 1.457737974 + -0.5

Combine like terms: 1.457737974 + -0.5 = 0.957737974
a = 0.957737974

Simplifying
a = 0.957737974

Subproblem 2
a + 0.5 = -1.457737974

Simplifying
a + 0.5 = -1.457737974

Reorder the terms:
0.5 + a = -1.457737974

Solving
0.5 + a = -1.457737974

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = -1.457737974 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -1.457737974 + -0.5
a = -1.457737974 + -0.5

Combine like terms: -1.457737974 + -0.5 = -1.957737974
a = -1.957737974

Simplifying
a = -1.957737974

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.957737974, -1.957737974}