0=6+15t-16t^2

Solution for 0=6+15t-16t^2 equation:

0=6+15t-16t^2

We move all terms to the left:

0-(6+15t-16t^2)=0

We add all the numbers together, and all the variables

-(6+15t-16t^2)=0

We get rid of parentheses

16t^2-15t-6=0

a = 16; b = -15; c = -6;
Δ = b2-4ac
Δ = -152-4·16·(-6)
Δ = 609
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{609}}{2*16}=\frac{15-\sqrt{609}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{609}}{2*16}=\frac{15+\sqrt{609}}{32}
$