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