SOLUTION: What is the correct set up for this problem and how do I arrive at answer of a = -1/3. 5a + 1/4a + 6 = 3/4 I figured the LCD to be 2(2a + 3) 2(2a + 3)* 5a + 1/2(2a + 3) =

Question 402215: What is the correct set up for this problem and how do I arrive at answer of a = -1/3.
5a + 1/4a + 6 = 3/4
I figured the LCD to be 2(2a + 3)
2(2a + 3)* 5a + 1/2(2a + 3) = 2(2a + 3)*3/4
= 5a + 1 = 2a + 3 * 3/2 (This is where I am having problem in solving this problem.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
5a + 1/(4a+6) = 3/4
5a + 1/(2(2a+3)) = 3/4
multiply both sides by 4(2a+3)
5a(4(2a+3)) + 2 = 3(2a+3)
5a(8a+12) + 2 = 3(2a+3)
40a^2+60a + 2 = 6a+9
40a^2+54a + 2 = 9
40a^2+54a-7 = 0
apply the "quadratic formula" to get:
a = {0.119, -1.469}
.
Details of quadratic:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=4036 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.11911900871343, -1.46911900871343. Here's your graph:

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