96t-16t^2=50

Solution for 96t-16t^2=50 equation:

96t-16t^2=50

We move all terms to the left:

96t-16t^2-(50)=0

a = -16; b = 96; c = -50;
Δ = b2-4ac
Δ = 962-4·(-16)·(-50)
Δ = 6016
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:

$\sqrt{\Delta}=\sqrt{6016}=\sqrt{64*94}=\sqrt{64}*\sqrt{94}=8\sqrt{94}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-8\sqrt{94}}{2*-16}=\frac{-96-8\sqrt{94}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+8\sqrt{94}}{2*-16}=\frac{-96+8\sqrt{94}}{-32}
$