8(z-3)2z=36

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

8(z-3)2z=36

We move all terms to the left:

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

We multiply parentheses

16z^2-48z-36=0

a = 16; b = -48; c = -36;
Δ = b2-4ac
Δ = -482-4·16·(-36)
Δ = 4608
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:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48\sqrt{2}}{2*16}=\frac{48-48\sqrt{2}}{32}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48\sqrt{2}}{2*16}=\frac{48+48\sqrt{2}}{32}
$