20=-16t*t+30t+1000

Solution for 20=-16t*t+30t+1000 equation:

20=-16t*t+30t+1000

We move all terms to the left:

20-(-16t*t+30t+1000)=0

We add all the numbers together, and all the variables

-(30t-16t*t+1000)+20=0

We get rid of parentheses

-30t+16t*t-1000+20=0

We add all the numbers together, and all the variables

-30t+16t*t-980=0

Wy multiply elements

16t^2-30t-980=0

a = 16; b = -30; c = -980;
Δ = b2-4ac
Δ = -302-4·16·(-980)
Δ = 63620
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:

$\sqrt{\Delta}=\sqrt{63620}=\sqrt{4*15905}=\sqrt{4}*\sqrt{15905}=2\sqrt{15905}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{15905}}{2*16}=\frac{30-2\sqrt{15905}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{15905}}{2*16}=\frac{30+2\sqrt{15905}}{32}
$