24t-t^2=8

Solution for 24t-t^2=8 equation:

24t-t^2=8

We move all terms to the left:

24t-t^2-(8)=0

We add all the numbers together, and all the variables

-1t^2+24t-8=0

a = -1; b = 24; c = -8;
Δ = b2-4ac
Δ = 242-4·(-1)·(-8)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{34}}{2*-1}=\frac{-24-4\sqrt{34}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{34}}{2*-1}=\frac{-24+4\sqrt{34}}{-2}
$