217=217-17t-16t^2

Solution for 217=217-17t-16t^2 equation:

217=217-17t-16t^2

We move all terms to the left:

217-(217-17t-16t^2)=0

We get rid of parentheses

16t^2+17t-217+217=0

We add all the numbers together, and all the variables

16t^2+17t=0

a = 16; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·16·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*16}=\frac{-34}{32}
=-1+1/16
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*16}=\frac{0}{32}
=0
$