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

Solution for (6+z)(3z+8)=0 equation:

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

We add all the numbers together, and all the variables

(z+6)(3z+8)=0

We multiply parentheses ..

(+3z^2+8z+18z+48)=0

We get rid of parentheses

3z^2+8z+18z+48=0

We add all the numbers together, and all the variables

3z^2+26z+48=0

a = 3; b = 26; c = +48;
Δ = b2-4ac
Δ = 262-4·3·48
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-10}{2*3}=\frac{-36}{6}
=-6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+10}{2*3}=\frac{-16}{6}
=-2+2/3
$