0=-16t^2+14t+17

Solution for 0=-16t^2+14t+17 equation:

0=-16t^2+14t+17

We move all terms to the left:

0-(-16t^2+14t+17)=0

We add all the numbers together, and all the variables

-(-16t^2+14t+17)=0

We get rid of parentheses

16t^2-14t-17=0

a = 16; b = -14; c = -17;
Δ = b2-4ac
Δ = -142-4·16·(-17)
Δ = 1284
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{321}}{2*16}=\frac{14-2\sqrt{321}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{321}}{2*16}=\frac{14+2\sqrt{321}}{32}
$