(9+z)(3z-1)=0

Solution for (9+z)(3z-1)=0 equation:

(9+z)(3z-1)=0

We add all the numbers together, and all the variables

(z+9)(3z-1)=0

We multiply parentheses ..

(+3z^2-1z+27z-9)=0

We get rid of parentheses

3z^2-1z+27z-9=0

We add all the numbers together, and all the variables

3z^2+26z-9=0

a = 3; b = 26; c = -9;
Δ = b2-4ac
Δ = 262-4·3·(-9)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-28}{2*3}=\frac{-54}{6}
=-9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+28}{2*3}=\frac{2}{6}
=1/3
$