4a^2+13a-24=0

Solution for 4a^2+13a-24=0 equation:

Simplifying
4a2 + 13a + -24 = 0

Reorder the terms:
-24 + 13a + 4a2 = 0

Solving
-24 + 13a + 4a2 = 0

Solving for variable 'a'.

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

Divide each side by '4'.
-6 + 3.25a + a2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3.25a + 6 + a2 = 0 + 6

Reorder the terms:
-6 + 6 + 3.25a + a2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 3.25a + a2 = 0 + 6
3.25a + a2 = 0 + 6

Combine like terms: 0 + 6 = 6
3.25a + a2 = 6

The a term is 3.25a.  Take half its coefficient (1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
3.25a + 2.640625 + a2 = 6 + 2.640625

Reorder the terms:
2.640625 + 3.25a + a2 = 6 + 2.640625

Combine like terms: 6 + 2.640625 = 8.640625
2.640625 + 3.25a + a2 = 8.640625

Factor a perfect square on the left side:
(a + 1.625)(a + 1.625) = 8.640625

Calculate the square root of the right side: 2.939494004

Break this problem into two subproblems by setting 
(a + 1.625) equal to 2.939494004 and -2.939494004.

Subproblem 1
a + 1.625 = 2.939494004

Simplifying
a + 1.625 = 2.939494004

Reorder the terms:
1.625 + a = 2.939494004

Solving
1.625 + a = 2.939494004

Solving for variable 'a'.

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

Add '-1.625' to each side of the equation.
1.625 + -1.625 + a = 2.939494004 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + a = 2.939494004 + -1.625
a = 2.939494004 + -1.625

Combine like terms: 2.939494004 + -1.625 = 1.314494004
a = 1.314494004

Simplifying
a = 1.314494004

Subproblem 2
a + 1.625 = -2.939494004

Simplifying
a + 1.625 = -2.939494004

Reorder the terms:
1.625 + a = -2.939494004

Solving
1.625 + a = -2.939494004

Solving for variable 'a'.

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

Add '-1.625' to each side of the equation.
1.625 + -1.625 + a = -2.939494004 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + a = -2.939494004 + -1.625
a = -2.939494004 + -1.625

Combine like terms: -2.939494004 + -1.625 = -4.564494004
a = -4.564494004

Simplifying
a = -4.564494004

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.314494004, -4.564494004}