50=-16t^2-20t+180

Solution for 50=-16t^2-20t+180 equation:

50=-16t^2-20t+180

We move all terms to the left:

50-(-16t^2-20t+180)=0

We get rid of parentheses

16t^2+20t-180+50=0

We add all the numbers together, and all the variables

16t^2+20t-130=0

a = 16; b = 20; c = -130;
Δ = b2-4ac
Δ = 202-4·16·(-130)
Δ = 8720
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:

$\sqrt{\Delta}=\sqrt{8720}=\sqrt{16*545}=\sqrt{16}*\sqrt{545}=4\sqrt{545}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{545}}{2*16}=\frac{-20-4\sqrt{545}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{545}}{2*16}=\frac{-20+4\sqrt{545}}{32}
$