0=-16t^2+10t+30

Solution for 0=-16t^2+10t+30 equation:

0=-16t^2+10t+30

We move all terms to the left:

0-(-16t^2+10t+30)=0

We add all the numbers together, and all the variables

-(-16t^2+10t+30)=0

We get rid of parentheses

16t^2-10t-30=0

a = 16; b = -10; c = -30;
Δ = b2-4ac
Δ = -102-4·16·(-30)
Δ = 2020
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:

$\sqrt{\Delta}=\sqrt{2020}=\sqrt{4*505}=\sqrt{4}*\sqrt{505}=2\sqrt{505}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{505}}{2*16}=\frac{10-2\sqrt{505}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{505}}{2*16}=\frac{10+2\sqrt{505}}{32}
$