0=-16t^2-20t+240

Solution for 0=-16t^2-20t+240 equation:

0=-16t^2-20t+240

We move all terms to the left:

0-(-16t^2-20t+240)=0

We add all the numbers together, and all the variables

-(-16t^2-20t+240)=0

We get rid of parentheses

16t^2+20t-240=0

a = 16; b = 20; c = -240;
Δ = b2-4ac
Δ = 202-4·16·(-240)
Δ = 15760
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:

$\sqrt{\Delta}=\sqrt{15760}=\sqrt{16*985}=\sqrt{16}*\sqrt{985}=4\sqrt{985}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{985}}{2*16}=\frac{-20-4\sqrt{985}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{985}}{2*16}=\frac{-20+4\sqrt{985}}{32}
$