0=7+24t-16t^2

Solution for 0=7+24t-16t^2 equation:

0=7+24t-16t^2

We move all terms to the left:

0-(7+24t-16t^2)=0

We add all the numbers together, and all the variables

-(7+24t-16t^2)=0

We get rid of parentheses

16t^2-24t-7=0

a = 16; b = -24; c = -7;
Δ = b2-4ac
Δ = -242-4·16·(-7)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-32}{2*16}=\frac{-8}{32}
=-1/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+32}{2*16}=\frac{56}{32}
=1+3/4
$