how do i solve this equation? 350+80t < 20∗2^t

40t^2-80t-350>0
8t^2 - 16t - 70 >0
Solve it as 8t^2-16t-70 = 0
Once you get the roots, you can find the regions for which the equation is positive.
For example, here the roots would be
{-16+Rt(256+2240)}/16 and {-16-Rt(256+2240)}/16
By wavy curve method, we can tell that the region on positive side of first root will be positive and the region on left side of second root will also be positive. Read a bit about wavy curve method to understand it better.
Thanks