24t=-16t^2+54t+24

Solution for 24t=-16t^2+54t+24 equation:

24t=-16t^2+54t+24

We move all terms to the left:

24t-(-16t^2+54t+24)=0

We get rid of parentheses

16t^2-54t+24t-24=0

We add all the numbers together, and all the variables

16t^2-30t-24=0

a = 16; b = -30; c = -24;
Δ = b2-4ac
Δ = -302-4·16·(-24)
Δ = 2436
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:

$\sqrt{\Delta}=\sqrt{2436}=\sqrt{4*609}=\sqrt{4}*\sqrt{609}=2\sqrt{609}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{609}}{2*16}=\frac{30-2\sqrt{609}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{609}}{2*16}=\frac{30+2\sqrt{609}}{32}
$