24(t)=50-16t^2

Solution for 24(t)=50-16t^2 equation:

24(t)=50-16t^2

We move all terms to the left:

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

We get rid of parentheses

16t^2+24t-50=0

a = 16; b = 24; c = -50;
Δ = b2-4ac
Δ = 242-4·16·(-50)
Δ = 3776
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:

$\sqrt{\Delta}=\sqrt{3776}=\sqrt{64*59}=\sqrt{64}*\sqrt{59}=8\sqrt{59}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{59}}{2*16}=\frac{-24-8\sqrt{59}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{59}}{2*16}=\frac{-24+8\sqrt{59}}{32}
$