50=16t^2-150t

Solution for 50=16t^2-150t equation:

50=16t^2-150t

We move all terms to the left:

50-(16t^2-150t)=0

We get rid of parentheses

-16t^2+150t+50=0

a = -16; b = 150; c = +50;
Δ = b2-4ac
Δ = 1502-4·(-16)·50
Δ = 25700
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:

$\sqrt{\Delta}=\sqrt{25700}=\sqrt{100*257}=\sqrt{100}*\sqrt{257}=10\sqrt{257}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-10\sqrt{257}}{2*-16}=\frac{-150-10\sqrt{257}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+10\sqrt{257}}{2*-16}=\frac{-150+10\sqrt{257}}{-32}
$