z(z+8)-9=2z(7-z)

Solution for z(z+8)-9=2z(7-z) equation:

z(z+8)-9=2z(7-z)

We move all terms to the left:

z(z+8)-9-(2z(7-z))=0

We add all the numbers together, and all the variables

z(z+8)-(2z(-1z+7))-9=0

We multiply parentheses

z^2+8z-(2z(-1z+7))-9=0


We calculate terms in parentheses: -(2z(-1z+7)), so:

2z(-1z+7)

We multiply parentheses

-2z^2+14z

Back to the equation:

-(-2z^2+14z)


We get rid of parentheses

z^2+2z^2-14z+8z-9=0

We add all the numbers together, and all the variables

3z^2-6z-9=0

a = 3; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·3·(-9)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12}{2*3}=\frac{-6}{6}
=-1
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12}{2*3}=\frac{18}{6}
=3
$