(2+z)(2z+5)=0

Solution for (2+z)(2z+5)=0 equation:

(2+z)(2z+5)=0

We add all the numbers together, and all the variables

(z+2)(2z+5)=0

We multiply parentheses ..

(+2z^2+5z+4z+10)=0

We get rid of parentheses

2z^2+5z+4z+10=0

We add all the numbers together, and all the variables

2z^2+9z+10=0

a = 2; b = 9; c = +10;
Δ = b2-4ac
Δ = 92-4·2·10
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-1}{2*2}=\frac{-10}{4}
=-2+1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+1}{2*2}=\frac{-8}{4}
=-2
$