0=105-9t-16t^2

Solution for 0=105-9t-16t^2 equation:

0=105-9t-16t^2

We move all terms to the left:

0-(105-9t-16t^2)=0

We add all the numbers together, and all the variables

-(105-9t-16t^2)=0

We get rid of parentheses

16t^2+9t-105=0

a = 16; b = 9; c = -105;
Δ = b2-4ac
Δ = 92-4·16·(-105)
Δ = 6801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{6801}}{2*16}=\frac{-9-\sqrt{6801}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{6801}}{2*16}=\frac{-9+\sqrt{6801}}{32}
$