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

Solution for (3+z)(5z+8)=0 equation:

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

We add all the numbers together, and all the variables

(z+3)(5z+8)=0

We multiply parentheses ..

(+5z^2+8z+15z+24)=0

We get rid of parentheses

5z^2+8z+15z+24=0

We add all the numbers together, and all the variables

5z^2+23z+24=0

a = 5; b = 23; c = +24;
Δ = b2-4ac
Δ = 232-4·5·24
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-7}{2*5}=\frac{-30}{10}
=-3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+7}{2*5}=\frac{-16}{10}
=-1+3/5
$