10=-16t^2+24t+5

Solution for 10=-16t^2+24t+5 equation:

10=-16t^2+24t+5

We move all terms to the left:

10-(-16t^2+24t+5)=0

We get rid of parentheses

16t^2-24t-5+10=0

We add all the numbers together, and all the variables

16t^2-24t+5=0

a = 16; b = -24; c = +5;
Δ = b2-4ac
Δ = -242-4·16·5
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16}{2*16}=\frac{8}{32}
=1/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16}{2*16}=\frac{40}{32}
=1+1/4
$