8(z+2)3z=36

Solution for 8(z+2)3z=36 equation:

8(z+2)3z=36

We move all terms to the left:

8(z+2)3z-(36)=0

We multiply parentheses

24z^2+48z-36=0

a = 24; b = 48; c = -36;
Δ = b2-4ac
Δ = 482-4·24·(-36)
Δ = 5760
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:

$\sqrt{\Delta}=\sqrt{5760}=\sqrt{576*10}=\sqrt{576}*\sqrt{10}=24\sqrt{10}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-24\sqrt{10}}{2*24}=\frac{-48-24\sqrt{10}}{48}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+24\sqrt{10}}{2*24}=\frac{-48+24\sqrt{10}}{48}
$