0=16t^2-205t-10

Solution for 0=16t^2-205t-10 equation:

0=16t^2-205t-10

We move all terms to the left:

0-(16t^2-205t-10)=0

We add all the numbers together, and all the variables

-(16t^2-205t-10)=0

We get rid of parentheses

-16t^2+205t+10=0

a = -16; b = 205; c = +10;
Δ = b2-4ac
Δ = 2052-4·(-16)·10
Δ = 42665
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{-(205)-\sqrt{42665}}{2*-16}=\frac{-205-\sqrt{42665}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(205)+\sqrt{42665}}{2*-16}=\frac{-205+\sqrt{42665}}{-32}
$