z(8-z)/6=-3

Solution for z(8-z)/6=-3 equation:

z(8-z)/6=-3

We move all terms to the left:

z(8-z)/6-(-3)=0

We add all the numbers together, and all the variables

z(-1z+8)/6-(-3)=0

We add all the numbers together, and all the variables

z(-1z+8)/6+3=0

We multiply all the terms by the denominator


z(-1z+8)+3*6=0

We add all the numbers together, and all the variables

z(-1z+8)+18=0

We multiply parentheses

-1z^2+8z+18=0

a = -1; b = 8; c = +18;
Δ = b2-4ac
Δ = 82-4·(-1)·18
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{34}}{2*-1}=\frac{-8-2\sqrt{34}}{-2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{34}}{2*-1}=\frac{-8+2\sqrt{34}}{-2}
$