0=-16t^2+14t+240

Solution for 0=-16t^2+14t+240 equation:

0=-16t^2+14t+240

We move all terms to the left:

0-(-16t^2+14t+240)=0

We add all the numbers together, and all the variables

-(-16t^2+14t+240)=0

We get rid of parentheses

16t^2-14t-240=0

a = 16; b = -14; c = -240;
Δ = b2-4ac
Δ = -142-4·16·(-240)
Δ = 15556
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:

$\sqrt{\Delta}=\sqrt{15556}=\sqrt{4*3889}=\sqrt{4}*\sqrt{3889}=2\sqrt{3889}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{3889}}{2*16}=\frac{14-2\sqrt{3889}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{3889}}{2*16}=\frac{14+2\sqrt{3889}}{32}
$