(2+z)(2z+9)=0

Solution for (2+z)(2z+9)=0 equation:

(2+z)(2z+9)=0

We add all the numbers together, and all the variables

(z+2)(2z+9)=0

We multiply parentheses ..

(+2z^2+9z+4z+18)=0

We get rid of parentheses

2z^2+9z+4z+18=0

We add all the numbers together, and all the variables

2z^2+13z+18=0

a = 2; b = 13; c = +18;
Δ = b2-4ac
Δ = 132-4·2·18
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-5}{2*2}=\frac{-18}{4}
=-4+1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+5}{2*2}=\frac{-8}{4}
=-2
$