0=-16t^2+30t+100

Solution for 0=-16t^2+30t+100 equation:

0=-16t^2+30t+100

We move all terms to the left:

0-(-16t^2+30t+100)=0

We add all the numbers together, and all the variables

-(-16t^2+30t+100)=0

We get rid of parentheses

16t^2-30t-100=0

a = 16; b = -30; c = -100;
Δ = b2-4ac
Δ = -302-4·16·(-100)
Δ = 7300
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:

$\sqrt{\Delta}=\sqrt{7300}=\sqrt{100*73}=\sqrt{100}*\sqrt{73}=10\sqrt{73}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{73}}{2*16}=\frac{30-10\sqrt{73}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{73}}{2*16}=\frac{30+10\sqrt{73}}{32}
$