5-24t=16t^2

Solution for 5-24t=16t^2 equation:

5-24t=16t^2

We move all terms to the left:

5-24t-(16t^2)=0

determiningTheFunctionDomain
-16t^2-24t+5=0

a = -16; b = -24; c = +5;
Δ = b2-4ac
Δ = -242-4·(-16)·5
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{14}}{2*-16}=\frac{24-8\sqrt{14}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{14}}{2*-16}=\frac{24+8\sqrt{14}}{-32}
$