(5z-9)(3+z)=0

Solution for (5z-9)(3+z)=0 equation:

(5z-9)(3+z)=0

We add all the numbers together, and all the variables

(5z-9)(z+3)=0

We multiply parentheses ..

(+5z^2+15z-9z-27)=0

We get rid of parentheses

5z^2+15z-9z-27=0

We add all the numbers together, and all the variables

5z^2+6z-27=0

a = 5; b = 6; c = -27;
Δ = b2-4ac
Δ = 62-4·5·(-27)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-24}{2*5}=\frac{-30}{10}
=-3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+24}{2*5}=\frac{18}{10}
=1+4/5
$