First, let's simplify the left side of the equation:

(4x + 5)/2 - 13x^2 = 100 + 40x

(4x + 5)/2 - 13x^2 = 100 + 40x

(4x + 5)/2 - 13x^2 = 100 + 40x

2(4x + 5) - 26x^2 = 200 + 80x

8x + 10 - 26x^2 = 200 + 80x

Next, let's bring all terms to one side of the equation:

8x + 10 - 26x^2 - 200 - 80x = 0

-26x^2 - 72x - 190 = 0

Now, let's solve this quadratic equation.