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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

16t^2-100t-30=0

a = 16; b = -100; c = -30;
Δ = b2-4ac
Δ = -1002-4·16·(-30)
Δ = 11920
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:

$\sqrt{\Delta}=\sqrt{11920}=\sqrt{16*745}=\sqrt{16}*\sqrt{745}=4\sqrt{745}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{745}}{2*16}=\frac{100-4\sqrt{745}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{745}}{2*16}=\frac{100+4\sqrt{745}}{32}
$