I have no knowledge at all about catenary equations, I am only required to know the simple math. I am doing it for the main suspension cable of the golden gate bridge.
The equation for a catenary is $y=\frac12 a\left(e^{ax}+e^{−ax}\right)$, and the points are $(0,0), (640, 152),$ and $(-640,152)$. The website http://www.intmath.com/applications-integration/11-arc-length-curve.php used a "guess and check" method and got the equation $$y=1280\left(\frac{e^{x/1326} + e^{-x/1326}}{2} -1\right).$$
I plugged in $x=640$, $y=152$ and tried to solve for $a$, but it is not working. Is there a specific way to solve it?? Plzzz help this is for my math is... if there is no way, is there any way to form a catenaric equation without working with tension, force, and physics in general.