t=-16t^2+140t+30

Solution for t=-16t^2+140t+30 equation:

t=-16t^2+140t+30

We move all terms to the left:

t-(-16t^2+140t+30)=0

We get rid of parentheses

16t^2-140t+t-30=0

We add all the numbers together, and all the variables

16t^2-139t-30=0

a = 16; b = -139; c = -30;
Δ = b2-4ac
Δ = -1392-4·16·(-30)
Δ = 21241
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{-(-139)-\sqrt{21241}}{2*16}=\frac{139-\sqrt{21241}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-139)+\sqrt{21241}}{2*16}=\frac{139+\sqrt{21241}}{32}
$