(5z-1)(9+z)=0

Solution for (5z-1)(9+z)=0 equation:

(5z-1)(9+z)=0

We add all the numbers together, and all the variables

(5z-1)(z+9)=0

We multiply parentheses ..

(+5z^2+45z-1z-9)=0

We get rid of parentheses

5z^2+45z-1z-9=0

We add all the numbers together, and all the variables

5z^2+44z-9=0

a = 5; b = 44; c = -9;
Δ = b2-4ac
Δ = 442-4·5·(-9)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-46}{2*5}=\frac{-90}{10}
=-9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+46}{2*5}=\frac{2}{10}
=1/5
$