Ok i figured it out. Its actually pretty simple. so lets say you want to solve S(x) when x=11.8

what you do is u go to the table and look for where 11.8 is in between two values.

x a b c d

11.6000 0.7000 -0.4929 0.9431 -0.8393

12.0000 0.6000 -0.1413 -0.0640 0.0364

as you can see 11.8 fits between these two rows SOOO you take the values of the smaller row.

11.6000 0.7000 -0.4929 0.9431 -0.8393

and create the following equation for S(x)

then plug in the value u are solving for x=11.8