t=-16t^2-20t+140

Solution for t=-16t^2-20t+140 equation:

t=-16t^2-20t+140

We move all terms to the left:

t-(-16t^2-20t+140)=0

We get rid of parentheses

16t^2+20t+t-140=0

We add all the numbers together, and all the variables

16t^2+21t-140=0

a = 16; b = 21; c = -140;
Δ = b2-4ac
Δ = 212-4·16·(-140)
Δ = 9401
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{-(21)-\sqrt{9401}}{2*16}=\frac{-21-\sqrt{9401}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{9401}}{2*16}=\frac{-21+\sqrt{9401}}{32}
$