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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-2z^2+3z+16z-(2z+2)=0

We get rid of parentheses

-2z^2+3z+16z-2z-2=0

We add all the numbers together, and all the variables

-2z^2+17z-2=0

a = -2; b = 17; c = -2;
Δ = b2-4ac
Δ = 172-4·(-2)·(-2)
Δ = 273
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{273}}{2*-2}=\frac{-17-\sqrt{273}}{-4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{273}}{2*-2}=\frac{-17+\sqrt{273}}{-4}
$