(5z+2)(9+z)=0

Solution for (5z+2)(9+z)=0 equation:

(5z+2)(9+z)=0

We add all the numbers together, and all the variables

(5z+2)(z+9)=0

We multiply parentheses ..

(+5z^2+45z+2z+18)=0

We get rid of parentheses

5z^2+45z+2z+18=0

We add all the numbers together, and all the variables

5z^2+47z+18=0

a = 5; b = 47; c = +18;
Δ = b2-4ac
Δ = 472-4·5·18
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-43}{2*5}=\frac{-90}{10}
=-9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+43}{2*5}=\frac{-4}{10}
=-2/5
$