(8+z)(3z+7)=0

Solution for (8+z)(3z+7)=0 equation:

(8+z)(3z+7)=0

We add all the numbers together, and all the variables

(z+8)(3z+7)=0

We multiply parentheses ..

(+3z^2+7z+24z+56)=0

We get rid of parentheses

3z^2+7z+24z+56=0

We add all the numbers together, and all the variables

3z^2+31z+56=0

a = 3; b = 31; c = +56;
Δ = b2-4ac
Δ = 312-4·3·56
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-17}{2*3}=\frac{-48}{6}
=-8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+17}{2*3}=\frac{-14}{6}
=-2+1/3
$