340=-16t^2-4t+382

Solution for 340=-16t^2-4t+382 equation:

340=-16t^2-4t+382

We move all terms to the left:

340-(-16t^2-4t+382)=0

We get rid of parentheses

16t^2+4t-382+340=0

We add all the numbers together, and all the variables

16t^2+4t-42=0

a = 16; b = 4; c = -42;
Δ = b2-4ac
Δ = 42-4·16·(-42)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-52}{2*16}=\frac{-56}{32}
=-1+3/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+52}{2*16}=\frac{48}{32}
=1+1/2
$