8a^2+6a=15

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Solution for 8a^2+6a=15 equation:


Simplifying
8a2 + 6a = 15

Reorder the terms:
6a + 8a2 = 15

Solving
6a + 8a2 = 15

Solving for variable 'a'.

Reorder the terms:
-15 + 6a + 8a2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 6a + 8a2 = 0

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

Divide each side by '8'.
-1.875 + 0.75a + a2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + 0.75a + 1.875 + a2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + 0.75a + a2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + 0.75a + a2 = 0 + 1.875
0.75a + a2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
0.75a + a2 = 1.875

The a term is 0.75a.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75a + 0.140625 + a2 = 1.875 + 0.140625

Reorder the terms:
0.140625 + 0.75a + a2 = 1.875 + 0.140625

Combine like terms: 1.875 + 0.140625 = 2.015625
0.140625 + 0.75a + a2 = 2.015625

Factor a perfect square on the left side:
(a + 0.375)(a + 0.375) = 2.015625

Calculate the square root of the right side: 1.419727086

Break this problem into two subproblems by setting 
(a + 0.375) equal to 1.419727086 and -1.419727086.

Subproblem 1

a + 0.375 = 1.419727086 Simplifying a + 0.375 = 1.419727086 Reorder the terms: 0.375 + a = 1.419727086 Solving 0.375 + a = 1.419727086 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + a = 1.419727086 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + a = 1.419727086 + -0.375 a = 1.419727086 + -0.375 Combine like terms: 1.419727086 + -0.375 = 1.044727086 a = 1.044727086 Simplifying a = 1.044727086

Subproblem 2

a + 0.375 = -1.419727086 Simplifying a + 0.375 = -1.419727086 Reorder the terms: 0.375 + a = -1.419727086 Solving 0.375 + a = -1.419727086 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + a = -1.419727086 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + a = -1.419727086 + -0.375 a = -1.419727086 + -0.375 Combine like terms: -1.419727086 + -0.375 = -1.794727086 a = -1.794727086 Simplifying a = -1.794727086

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.044727086, -1.794727086}

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