24=4+44t-16t^2

Solution for 24=4+44t-16t^2 equation:

24=4+44t-16t^2

We move all terms to the left:

24-(4+44t-16t^2)=0

We get rid of parentheses

16t^2-44t-4+24=0

We add all the numbers together, and all the variables

16t^2-44t+20=0

a = 16; b = -44; c = +20;
Δ = b2-4ac
Δ = -442-4·16·20
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{41}}{2*16}=\frac{44-4\sqrt{41}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{41}}{2*16}=\frac{44+4\sqrt{41}}{32}
$