0=-16t^2+17t-4

Solution for 0=-16t^2+17t-4 equation:

0=-16t^2+17t-4

We move all terms to the left:

0-(-16t^2+17t-4)=0

We add all the numbers together, and all the variables

-(-16t^2+17t-4)=0

We get rid of parentheses

16t^2-17t+4=0

a = 16; b = -17; c = +4;
Δ = b2-4ac
Δ = -172-4·16·4
Δ = 33
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{-(-17)-\sqrt{33}}{2*16}=\frac{17-\sqrt{33}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{33}}{2*16}=\frac{17+\sqrt{33}}{32}
$