-16t^2-40t+100=t

Solution for -16t^2-40t+100=t equation:

-16t^2-40t+100=t

We move all terms to the left:

-16t^2-40t+100-(t)=0

We add all the numbers together, and all the variables

-16t^2-41t+100=0

a = -16; b = -41; c = +100;
Δ = b2-4ac
Δ = -412-4·(-16)·100
Δ = 8081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-\sqrt{8081}}{2*-16}=\frac{41-\sqrt{8081}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{8081}}{2*-16}=\frac{41+\sqrt{8081}}{-32}
$