6z(2z+8)=24

Solution for 6z(2z+8)=24 equation:

6z(2z+8)=24

We move all terms to the left:

6z(2z+8)-(24)=0

We multiply parentheses

12z^2+48z-24=0

a = 12; b = 48; c = -24;
Δ = b2-4ac
Δ = 482-4·12·(-24)
Δ = 3456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-24\sqrt{6}}{2*12}=\frac{-48-24\sqrt{6}}{24}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+24\sqrt{6}}{2*12}=\frac{-48+24\sqrt{6}}{24}
$