50t=-16t^2

Solution for 50t=-16t^2 equation:

50t=-16t^2

We move all terms to the left:

50t-(-16t^2)=0

We get rid of parentheses

16t^2+50t=0

a = 16; b = 50; c = 0;
Δ = b2-4ac
Δ = 502-4·16·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-50}{2*16}=\frac{-100}{32}
=-3+1/8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50}{2*16}=\frac{0}{32}
=0
$