0=100+10t-16t^2

Solution for 0=100+10t-16t^2 equation:

0=100+10t-16t^2

We move all terms to the left:

0-(100+10t-16t^2)=0

We add all the numbers together, and all the variables

-(100+10t-16t^2)=0

We get rid of parentheses

16t^2-10t-100=0

a = 16; b = -10; c = -100;
Δ = b2-4ac
Δ = -102-4·16·(-100)
Δ = 6500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6500}=\sqrt{100*65}=\sqrt{100}*\sqrt{65}=10\sqrt{65}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{65}}{2*16}=\frac{10-10\sqrt{65}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{65}}{2*16}=\frac{10+10\sqrt{65}}{32}
$