24=-16t^2+48t+110

Solution for 24=-16t^2+48t+110 equation:

24=-16t^2+48t+110

We move all terms to the left:

24-(-16t^2+48t+110)=0

We get rid of parentheses

16t^2-48t-110+24=0

We add all the numbers together, and all the variables

16t^2-48t-86=0

a = 16; b = -48; c = -86;
Δ = b2-4ac
Δ = -482-4·16·(-86)
Δ = 7808
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:

$\sqrt{\Delta}=\sqrt{7808}=\sqrt{64*122}=\sqrt{64}*\sqrt{122}=8\sqrt{122}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{122}}{2*16}=\frac{48-8\sqrt{122}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{122}}{2*16}=\frac{48+8\sqrt{122}}{32}
$