(8z+5)(5z+9)=0

Solution for (8z+5)(5z+9)=0 equation:

(8z+5)(5z+9)=0

We multiply parentheses ..

(+40z^2+72z+25z+45)=0

We get rid of parentheses

40z^2+72z+25z+45=0

We add all the numbers together, and all the variables

40z^2+97z+45=0

a = 40; b = 97; c = +45;
Δ = b2-4ac
Δ = 972-4·40·45
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(97)-47}{2*40}=\frac{-144}{80}
=-1+4/5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(97)+47}{2*40}=\frac{-50}{80}
=-5/8
$