0=-16t^2-10t+140

Solution for 0=-16t^2-10t+140 equation:

0=-16t^2-10t+140

We move all terms to the left:

0-(-16t^2-10t+140)=0

We add all the numbers together, and all the variables

-(-16t^2-10t+140)=0

We get rid of parentheses

16t^2+10t-140=0

a = 16; b = 10; c = -140;
Δ = b2-4ac
Δ = 102-4·16·(-140)
Δ = 9060
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:

$\sqrt{\Delta}=\sqrt{9060}=\sqrt{4*2265}=\sqrt{4}*\sqrt{2265}=2\sqrt{2265}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{2265}}{2*16}=\frac{-10-2\sqrt{2265}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{2265}}{2*16}=\frac{-10+2\sqrt{2265}}{32}
$