-8z^2-4z+24=0

Solution for -8z^2-4z+24=0 equation:

-8z^2-4z+24=0

a = -8; b = -4; c = +24;
Δ = b2-4ac
Δ = -42-4·(-8)·24
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-28}{2*-8}=\frac{-24}{-16}
=1+1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+28}{2*-8}=\frac{32}{-16}
=-2
$