15a^2+9a-16=0

Solution for 15a^2+9a-16=0 equation:

Simplifying
15a2 + 9a + -16 = 0

Reorder the terms:
-16 + 9a + 15a2 = 0

Solving
-16 + 9a + 15a2 = 0

Solving for variable 'a'.

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

Divide each side by '15'.
-1.066666667 + 0.6a + a2 = 0

Move the constant term to the right:

Add '1.066666667' to each side of the equation.
-1.066666667 + 0.6a + 1.066666667 + a2 = 0 + 1.066666667

Reorder the terms:
-1.066666667 + 1.066666667 + 0.6a + a2 = 0 + 1.066666667

Combine like terms: -1.066666667 + 1.066666667 = 0.000000000
0.000000000 + 0.6a + a2 = 0 + 1.066666667
0.6a + a2 = 0 + 1.066666667

Combine like terms: 0 + 1.066666667 = 1.066666667
0.6a + a2 = 1.066666667

The a term is 0.6a.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6a + 0.09 + a2 = 1.066666667 + 0.09

Reorder the terms:
0.09 + 0.6a + a2 = 1.066666667 + 0.09

Combine like terms: 1.066666667 + 0.09 = 1.156666667
0.09 + 0.6a + a2 = 1.156666667

Factor a perfect square on the left side:
(a + 0.3)(a + 0.3) = 1.156666667

Calculate the square root of the right side: 1.075484387

Break this problem into two subproblems by setting 
(a + 0.3) equal to 1.075484387 and -1.075484387.

Subproblem 1
a + 0.3 = 1.075484387

Simplifying
a + 0.3 = 1.075484387

Reorder the terms:
0.3 + a = 1.075484387

Solving
0.3 + a = 1.075484387

Solving for variable 'a'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + a = 1.075484387 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + a = 1.075484387 + -0.3
a = 1.075484387 + -0.3

Combine like terms: 1.075484387 + -0.3 = 0.775484387
a = 0.775484387

Simplifying
a = 0.775484387

Subproblem 2
a + 0.3 = -1.075484387

Simplifying
a + 0.3 = -1.075484387

Reorder the terms:
0.3 + a = -1.075484387

Solving
0.3 + a = -1.075484387

Solving for variable 'a'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + a = -1.075484387 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + a = -1.075484387 + -0.3
a = -1.075484387 + -0.3

Combine like terms: -1.075484387 + -0.3 = -1.375484387
a = -1.375484387

Simplifying
a = -1.375484387

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.775484387, -1.375484387}