0=123-11t-16t^2

Solution for 0=123-11t-16t^2 equation:

0=123-11t-16t^2

We move all terms to the left:

0-(123-11t-16t^2)=0

We add all the numbers together, and all the variables

-(123-11t-16t^2)=0

We get rid of parentheses

16t^2+11t-123=0

a = 16; b = 11; c = -123;
Δ = b2-4ac
Δ = 112-4·16·(-123)
Δ = 7993
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{-(11)-\sqrt{7993}}{2*16}=\frac{-11-\sqrt{7993}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{7993}}{2*16}=\frac{-11+\sqrt{7993}}{32}
$