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

Solution for 50(t)=-16t^2+t equation:

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

We move all terms to the left:

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

We get rid of parentheses

16t^2-t+50t=0

We add all the numbers together, and all the variables

16t^2+49t=0

a = 16; b = 49; c = 0;
Δ = b2-4ac
Δ = 492-4·16·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-49}{2*16}=\frac{-98}{32}
=-3+1/16
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+49}{2*16}=\frac{0}{32}
=0
$