24x^2-8x-192=0

Solution for 24x^2-8x-192=0 equation:

24x^2-8x-192=0

a = 24; b = -8; c = -192;
Δ = b2-4ac
Δ = -82-4·24·(-192)
Δ = 18496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18496}=136$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-136}{2*24}=\frac{-128}{48}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+136}{2*24}=\frac{144}{48}
=3
$