(4z+6)(9+z)=0

Solution for (4z+6)(9+z)=0 equation:

(4z+6)(9+z)=0

We add all the numbers together, and all the variables

(4z+6)(z+9)=0

We multiply parentheses ..

(+4z^2+36z+6z+54)=0

We get rid of parentheses

4z^2+36z+6z+54=0

We add all the numbers together, and all the variables

4z^2+42z+54=0

a = 4; b = 42; c = +54;
Δ = b2-4ac
Δ = 422-4·4·54
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-30}{2*4}=\frac{-72}{8}
=-9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+30}{2*4}=\frac{-12}{8}
=-1+1/2
$