8-6(9+4z)z=5

Solution for 8-6(9+4z)z=5 equation:

8-6(9+4z)z=5

We move all terms to the left:

8-6(9+4z)z-(5)=0

We add all the numbers together, and all the variables

-6(4z+9)z+8-5=0

We add all the numbers together, and all the variables

-6(4z+9)z+3=0

We multiply parentheses

-24z^2-54z+3=0

a = -24; b = -54; c = +3;
Δ = b2-4ac
Δ = -542-4·(-24)·3
Δ = 3204
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:

$\sqrt{\Delta}=\sqrt{3204}=\sqrt{36*89}=\sqrt{36}*\sqrt{89}=6\sqrt{89}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{89}}{2*-24}=\frac{54-6\sqrt{89}}{-48}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{89}}{2*-24}=\frac{54+6\sqrt{89}}{-48}
$