20t-4.9t^2=-100

Solution for 20t-4.9t^2=-100 equation:

20t-4.9t^2=-100

We move all terms to the left:

20t-4.9t^2-(-100)=0

We add all the numbers together, and all the variables

-4.9t^2+20t+100=0

a = -4.9; b = 20; c = +100;
Δ = b2-4ac
Δ = 202-4·(-4.9)·100
Δ = 2360
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:

$\sqrt{\Delta}=\sqrt{2360}=\sqrt{4*590}=\sqrt{4}*\sqrt{590}=2\sqrt{590}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{590}}{2*-4.9}=\frac{-20-2\sqrt{590}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{590}}{2*-4.9}=\frac{-20+2\sqrt{590}}{-9.8}
$