25=-16t^2-80t+121

Solution for 25=-16t^2-80t+121 equation:

25=-16t^2-80t+121

We move all terms to the left:

25-(-16t^2-80t+121)=0

We get rid of parentheses

16t^2+80t-121+25=0

We add all the numbers together, and all the variables

16t^2+80t-96=0

a = 16; b = 80; c = -96;
Δ = b2-4ac
Δ = 802-4·16·(-96)
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-112}{2*16}=\frac{-192}{32}
=-6
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+112}{2*16}=\frac{32}{32}
=1
$