-100=24t-4t^2

Solution for -100=24t-4t^2 equation:

-100=24t-4t^2

We move all terms to the left:

-100-(24t-4t^2)=0

We get rid of parentheses

4t^2-24t-100=0

a = 4; b = -24; c = -100;
Δ = b2-4ac
Δ = -242-4·4·(-100)
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{34}}{2*4}=\frac{24-8\sqrt{34}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{34}}{2*4}=\frac{24+8\sqrt{34}}{8}
$