32+16t-16t^2=t

Solution for 32+16t-16t^2=t equation:

32+16t-16t^2=t

We move all terms to the left:

32+16t-16t^2-(t)=0

We add all the numbers together, and all the variables

-16t^2+15t+32=0

a = -16; b = 15; c = +32;
Δ = b2-4ac
Δ = 152-4·(-16)·32
Δ = 2273
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{-(15)-\sqrt{2273}}{2*-16}=\frac{-15-\sqrt{2273}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{2273}}{2*-16}=\frac{-15+\sqrt{2273}}{-32}
$