0=3+33t-16t2

Solution for 0=3+33t-16t2 equation:

0=3+33t-16t^2

We move all terms to the left:

0-(3+33t-16t^2)=0

We add all the numbers together, and all the variables

-(3+33t-16t^2)=0

We get rid of parentheses

16t^2-33t-3=0

a = 16; b = -33; c = -3;
Δ = b2-4ac
Δ = -332-4·16·(-3)
Δ = 1281
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{-(-33)-\sqrt{1281}}{2*16}=\frac{33-\sqrt{1281}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1281}}{2*16}=\frac{33+\sqrt{1281}}{32}
$