8t^2+384t-13824=0

Solution for 8t^2+384t-13824=0 equation:

8t^2+384t-13824=0

a = 8; b = 384; c = -13824;
Δ = b2-4ac
Δ = 3842-4·8·(-13824)
Δ = 589824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{589824}=768$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(384)-768}{2*8}=\frac{-1152}{16}
=-72
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(384)+768}{2*8}=\frac{384}{16}
=24
$