0=-16t*t+9t+105

Solution for 0=-16t*t+9t+105 equation:

0=-16t*t+9t+105

We move all terms to the left:

0-(-16t*t+9t+105)=0

We add all the numbers together, and all the variables

-(9t-16t*t+105)+0=0

We add all the numbers together, and all the variables

-(9t-16t*t+105)=0

We get rid of parentheses

-9t+16t*t-105=0

Wy multiply elements

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}
$