0=6+17t-16t^2

Solution for 0=6+17t-16t^2 equation:

0=6+17t-16t^2

We move all terms to the left:

0-(6+17t-16t^2)=0

We add all the numbers together, and all the variables

-(6+17t-16t^2)=0

We get rid of parentheses

16t^2-17t-6=0

a = 16; b = -17; c = -6;
Δ = b2-4ac
Δ = -172-4·16·(-6)
Δ = 673
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{673}}{2*16}=\frac{17-\sqrt{673}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{673}}{2*16}=\frac{17+\sqrt{673}}{32}
$